India has tremendous sources of agate from the Deccan traps, a series of layered lava flows across 100s of square miles. I don't know of lava flows in Egypt or other countries in the Middle East, but there are likely some present which could have been the source of the brown agate of the Israelites. Amethyst is a purple variety of crystalline quartz, very similar to our own colorless rock crystal. Amethyst commonly forms as linings and fillings of gas cavities in igneous rock in a manner similar to agate, but as crystals, not as coatings of silica. Again, I can find no source in the immediate area of the Middle East, but amethyst is occasionally recovered from India, but is not a particularly common mineral there.
Citrine is a yellow variety of crystalline quartz, similar to amethyst and rock crystal.
The natural color may vary from brownish yellow to golden yellow to honey yellow to pale almost colorless yellow. However, it has been known from early times that by heating poorly colored or pale amethyst, you can produce golden to orange citrine. Natural crystals of citrine are truly uncommon. It is a mineral which again is sometimes encountered as infillings or crystals in gas cavities in lava flows. I could find no local source in the Middle East.