What type of capacitor would I need for a 50-watt 127v HPF HPS ballast? Part Number PBCC05SXH6031. It says 26OMFD at 400V but that seems high. Also, can someone decode the part number?

26uF/400V is very strange for a 50W ballast. If it is a series reactor and the cap is just parallel to the mains as a means to correct the power factor, the 26uF seems to be OK, but then I would expect lower voltage rating, like 150..200V or so (include derating to get reasonable lifetime). A 400V rated capacitor I would expect on some multivolt HX transformer type, but then the capacitance would be around 5..7uF.

If the capacitor is connected directly to the mains input (in your installation) and a NPF operation is not an issue, you may just omit the capacitor whatsoever.
Are you sure you are dealing with a S68 ballast?

It is an s68 HPF Reactor ballast.

So without the cap it will become an S68 NPF ballast feeding the lamp completely normally...

Low watt US HPS reactor ballasts have what seems to be high uF requirements...this is normal for line side PFC applications. The given voltage is just the dielectric rating of the capacitor. A capacitor rated for 150V maximum would also work.