If I grok the patch then I suggest:

mvn install -Ptest-on-installed-app -Dtest.profileName=eclipse -Dtest.installPath=/home/user/some/path/

Since
a) its during tests (just test-on instead of run-on)
b) test.profileName since it is just not part of tycho.surefire namespace
c) test.installPath because of same reason as #b and that installPath is the name.

and the short hand from this would be:
mvn install -Ptest-on-installed-app -Dtest.installPath=/home/user/some/path/

which is fine for this case where it is used for specifc test runs (not daily).