[Note: I have reposted this after the Forum "crash", as I just happened to still have a copy in notepad. It's more or less, what I originally posted. Unfortunately, SilverFox's and Henry's response to both our posts, are still missing.:sigh:]
Hi Henry. Most UltraFire products are a bit of a gamble, as far as quality goes. This applies especially to their Li-Ion cells. Most likely your 16340 cells are not able to supply ample current (ie. they suffer from severe voltage sag) to run the TwinTask for longer than they do.
I also own one of these lights that I keep in my car. I only use it with CR123A primary cells (one in the light, and one spare), as that is what the light is designed around, and primary cell shelf life is superior to that of Li-Ion cells. The light almost never gets used, as I always have a "pocket light" on my person, as well.
I would think that if you were to power it with a Li-Ion cell of good quality, the incandescent bulb would probably blow, sooner, rather than later. In addition, the LEDs would be over driven. This is due to the fact that primary cells have a nominal voltage under load of somewhat less than 3 Volts, in most applications. Most Li-Ion cells have a nominal voltage of 3.6-3.7 Volts. Therefore, I think you'd be better off just sticking with primary cells for use in your TwinTask TT-1L.
If you really want to use Li-Ion cells, you can replace the incan bulb with a 5mm LED. I did this a few years back. The light is not all that bright, as you have replaced the "high" (incan bulb) with a single 5mm LED. It will run a long time on one LED and quite a while on the 3 LEDs, but the other downside is, as I said, the LEDs are over driven and probably won't last very long. Also, the runtime on the 3 LEDs is much less, as the capacity of a Li-Ion cell is no match for a primary cell and in addition, the drive current is higher due to the higher voltage, further reducing the runtime. It is for these reasons I went back to the original configuration with mine, and use it "as is".
Dave