Question: In what month did the both the Battle of Kulcullen occur and the Irish Rebellion start?

Context articles: The Boys of Wexford
HMS Wilhelmina (1798)
Robert Hovenden (Ireland)
Irish Rebellion of 1798
John Byng, 1st Earl of Strafford
Battle of Vinegar Hill
Order of battle at the Battle of Tory Island
Battle of Foulksmills
Action of 24 October 1798
Battle of Kilcullen

"The Boys of Wexford" (also known as "The Flight of the Earls") is an Irish ballad commemorating the Irish Rebellion of 1798 and, more specifically, the Wexford Rebellion.
 The aim of rebellion was to remove English control from Irish affairs and it resulted in the 1801 Act of Union.
HMS "Wilhelmina" was a 32-gun fifth rate frigate of the Royal Navy.
 She was previously a Dutch ship and had been built in 1787 for the Dutch Republic as the "Wilhelmina".
 She was renamed "Furie" in 1795, after the establishment of the Batavian Republic as a client state of the First French Empire.
 Like other Dutch ships at that time, she was pressed into service as part of French plans to support the Irish Rebellion of 1798 in the hope of destabilising Britain.
 The British captured her and the Dutch corvette "Waakzaamheid" in 1798 while the two were supporting French and Irish forces involved in the Irish Rebellion.
 The Royal Navy took both into service, with "Furie" regaining her original name.
 Sailing as HMS "Wilhelmina", she spent the bulk of her later career in the East Indies, serving mostly as a troopship.
 Here she fought an unequal battle against a large French privateer, and succeeded in driving her off and protecting a merchant she was escorting.
 "Wilhelmina" was almost the ship that faced a superior French squadron at the Battle of Vizagapatam, but she was replaced beforehand by the larger HMS "Centurion" .
 She spent the rest of her days as a guardship in Penang, and was sold there in 1813.
Robert Hovenden or Robert Hovendon was an Irish figure who participated in the Irish Rebellion of 1641.
 Hovenden was the half-brother of Sir Phelim O'Neill, a prime inistigator in the Ulster-centred rebellion.
 Although Hovenden was of New English descent, he was a Roman Catholic like many of the other Hovenden settlers in Ireland.
 His father (also known as Robert Hovenden) had in 1613 married the widow of Sir Turlough MacShane O'Neill of County Tyrone who had been killed while serving on the Crown's side in O'Doherty's Rebellion.
 The family acquired property in Kinard some of which was Hovendon's, although Sir Phelim as the heir to his father was the dominant figure in the area and sat in Irish Parliament as member for Dungannon.
The Irish Rebellion of 1798 (Irish: "Éirí Amach 1798" ), also known as the United Irishmen Rebellion (Irish: "Éirí Amach na nÉireannach Aontaithe" ), was an uprising against British rule in Ireland lasting from May to September 1798.
 The United Irishmen, a republican revolutionary group influenced by the ideas of the American and French revolutions, were the main organising force behind the rebellion.
Field Marshal John Byng, 1st Earl of Strafford (1772 – 3 June 1860) was a British Army officer and politician.
 After serving as a junior officer during the French Revolutionary Wars and Irish Rebellion of 1798, he became Commanding Officer of the Grenadier Battalion of the 3rd Regiment of Foot Guards during the disastrous Walcheren Campaign.
 He served as a brigade commander at the Battle of Vitoria and then at the Battle of Roncesvalles on 25 July 1813 when his brigade took the brunt of the French assault and held its position for three hours in the early morning before finally being forced back.
 During the Hundred Days he commanded the 2nd Guards Brigade at the Battle of Quatre Bras in June 1815 and again at the Battle of Waterloo later that month when light companies from his brigade played an important role in the defence of Château d'Hougoumont.
 He went on to be Commander-in-Chief, Ireland and, after leaving Ireland in 1831, he was elected as Whig Member of Parliament for Poole in Dorset and was one of the few military men who supported the Reform Bill, for which he was rewarded with a peerage.
The Battle of Vinegar Hill ("Irish": Cath Chnoc Fhíodh na gCaor), was an engagement during the Irish Rebellion of 1798 on 21 June 1798 when over 13,000 British soldiers launched an attack on Vinegar Hill outside Enniscorthy, County Wexford, the largest camp and headquarters of the Wexford United Irish rebels.
 It marked a turning point in the rebellion, as it was the last attempt by the rebels to hold and defend ground against the British military.
 The battle was actually fought in two locations: on Vinegar Hill itself and in the streets of nearby Enniscorthy.
The Battle of Tory Island, (also known as the Battle of Donegal, Battle of Lough Swilly and Warren's Action) was a naval action fought on 12 October 1798 off the north coast of Ireland.
 The battle contested an attempted French invasion of Donegal in support of the Irish Rebellion of 1798, with a French squadron under Jean-Baptiste-François Bompart facing a hastily assembled Royal Navy blockade squadron under Sir John Borlase Warren.
 Bompart's force had been dispatched from Brest the month before with orders to reinforce a French army under Jean Humbert which had landed two months earlier.
The Battle of Foulksmills, known locally as the Battle of Horetown and also known as the Battle of Goff's Bridge, was a battle on 20 June 1798 between advancing British forces seeking to stamp out the rebellion in County Wexford during the Irish Rebellion of 1798 and a rebel army assembled to oppose them.
The Action of 24 October 1798 was a minor naval engagement of the French Revolutionary Wars, fought between a British Royal Navy frigate and two ships of the Batavian Republic.
 The Dutch ships were intercepted in the North Sea within hours of leaving port, 30 nmi northwest of the Texel, by the British ship HMS "Sirius".
 Both Dutch vessels were carrying large quantities of military supplies and French soldiers, reinforcements for the French and Irish forces participating in the Irish Rebellion of 1798.
 Although the rebellion had been defeated a month earlier, word of the British victory had not yet reached the European continent, and the Dutch force was intended to supplement a larger French squadron sent earlier in October.
 The French had already been defeated at the Battle of Tory Island and the Dutch suffered a similar outcome, both ships defeated in turn by the larger and better armed British vessel.
The outbreak of the rebellion on the night of 23/24 May 1798 led to failed assaults on Ballymore-Eustace, Naas, and Prosperous.
 As news of the rising spread throughout Kildare, Kilcullen rebels began to mobilise in the ancient hill-top churchyard in the townland now known as Old Kilcullen.
 About 200 had gathered by daybreak, including a number of survivors of the attack on Ballymore-Eustace, when they were spotted by local military under the command of Lieutenant General Ralph Dundas, Commander of the Army of the Midlands, whose headquarters, Castle Martin, was located only three miles away.
 Dundas quickly mustered a combined force of about 120 infantry, cavalry and dragoons and marched to disperse the rebel gathering.