What regulation requires a soldier to participate in training after they complete a separation physical before they ETS?

I would approach this from the angle of "What is the worst that can happen?" If this troop gets hurt after completing the final SEPS physical, it will create much headache for you and your unit.
If you are talking about routine training, like daily PT, he should be expected to participate until he detaches. Anything beyond that he is just a risk that can be avoided. This is a good opportunity to show good judgement. Is sending SPC Goofinhiemer to go to the rifle range a week before ETS a priority? Probably not. Think risk vs reward.
Additionally, your unit should have a policy in place regarding this issue. As an NCO you need to know what your unit commander expects.

Simply counsel him he better participate or that his rank (unless he's an E1) can be lower. In the US Armed Forces the offence is covered by article 134 (the "general article") of the Uniform Code of Military Justice (UCMJ). Its prejudicial of good order and discipline. You're going to have more of this as you advance in rank.

"There are no limitations placed upon Soldiers or commanders after a Phase 2 physical has been completed unless the Soldier has a profile with limitations that clearly and thoroughly outline those limitations. Soldiers are required to continue to participate in PT."

http://www.forthoodsentinel.com/news/phase-2-physicals-when-completed-does-it-place-limitations-on-soldiers-or-commanders/article_54279128-10be-559d-9e56-1606cb909838.html