Here's the situation. Barrel dimpling jigs are $$ and I would rather spend the time than the money.

That would be fine as long as you can hit dead center when you cross drill.

This ^^^

Nothing wrong with doing it on the lathe, you just have to be sure you get it indicated in properly. That is a classic case of using "the wrong tool for the job". Sometimes using the wrong tool will still work, but most of the time it is a lot more difficult and challenging. If you're up for it I see no problem with trying...

Would using a dead center in the tailstock to pinch a ruler against the work piece in the chuck work for finding center? Or do I need to use indicators?

I wish I had a decent drill press. I have a tiny little ryobi that has plenty of wobble. I use it for all kinds of things, but nothing that needs to be precise. And by the time I bought decent V blocks I could just buy the dimpling jig itself from brownells.

That depends how precise you want your holes located for the dimpling jig. Your holes will only be located as precisely as all of your errors combined. If you have a sloppy old lathe you will have a .005-.020 error (depending on technique and how bad your lathe is) just on getting a drill-bit started in the work-piece. If you add on another .050" by using only a ruler to locate your work-piece into the 4-jaw you could end up with a total tolerance stackup of .140" (over 1/8"). Are you ok with that? How close and how repeatable can you get a workpiece into your 4-jaw using a ruler?

From my understanding he has the stock already to size, he just needs to drill the 2 dimpling holes into it in a precise manner.

Your post does bring up a good point though. You can "clamp" the stock to your cross-slide and use the cross-slide to get the holes precisely spaced. Use shim-stock under the work-piece to get it to the right height, drill first hole, crank cross-slide the right distance and drill second hole (with drill bit in the head-stock).