The TSP-2AA can't be used like a twisty because there is a spring on the Kroll which pushes the batteries forward as you screw the TSP outwards. I got rid of the spring when I took out the Kroll, which just leaves a threaded hole.
The Maglite tail cap which replaces the Kroll has no spring inside, just an empty hole. You need to put something metallic (i.e. conductive) in the hole which protrudes outward to act as the pusher against the battery like central post in a twisty. Then you can adjust the length of whatever you put in there (that is, make it a little long and file it to the correct length) so that the light comes on after the TSP-2AA is screwed into the Arc body a reasonable distance..
I found that my Arc TSP-123 twisty tail would light up about 2 1/2 turns from the point where the threads first engage the body. I scrounged around and found a small cylindrical piece of steel about 1/4" in diameter and about 11/16" long (these are eyeball measurements, no calipers or anything) which would press fit into the hole in my Maglite tail cap and which protruded about 3/16" past the end of the Maglite tail cap. I pushed this into the hole and screwed the tail cap all the way in (a little grease helps as the tail cap threads were dry- I used a very little graphite based grease on the theory it might be conductive and it worked well).
In my case, this little piece of steel turned out to be just about right and the TSP-2AA/Maglite twisty would turn on 2 1/2 turns after the threads engage. I therefore now have a good-as-Arc-factory TSP-2AA twisty body (just a little longer) with a very nice lanyard hole in it; and I have no more Kroll switch concerns (my Kroll at least was tempermental).
All you need to do is find something about that size which can be adjusted (i.e. filed) to do the same. For the record, what I used was the decapping pin retaining nut from a set of Lyman 310 Tong Tool reloading dies, which I doubt you will have one of lying around. However, pretty much anything of about those dimensions should do fine.
Hope this helps. Good luck.