Is there a volunteer roster out there, other than MOBCOP/Tour of Duty? And if so how do you get on it?

Prepare for a roster list of "When I deployed, we were just told!"

You can click the "volunteer" button on HRC; which as far as I can tell does absolutely nothing, I've had it clicked for near a decade and haven't heard a peep. No, there isn't an Army-wide list they just pull people for, to answer your question directly.

Your best solution, far as I've seen others actually be successful at, is to talk to your career counselor and neighboring units. Someone, somewhere will have a slot that isn't advertised on MOBCOP for whatever reason, and put you in it. Takes a lot of networking.

Reality is, Army isn't struggling for people to deploy, Active has everything well in hand right now-- especially as the mission over there isn't even a tenth of what the manning was a decade ago.

you can be a volunteer thru HRCs website.

I was asked if I wanted to go TDY by my detachment SGM. I said yes,
2 weeks later I was in Saudi Arabia for desert storm

First off watch what you wish for! In 2013 before I was kicked off AKO there was an area in the HRC home pages that you could search for openings , tours etc. Remember regardless unless your IRR you'll still have to get permission/ realeased from your current unit and it's not automatic upon your return that you can get back in that same unit you left! Good luck in your quest!