This thread has made me do some looking around for myself.
Here are some comments about the iTP A1 EOS CR123 (and some comparisons with the other two models in the family).
1) The A1 uses a CR123 battery (or the rechargeable RCR123 or 16340). The A2 (AA) and A3 (AAA) do not.
2) The weights, with battery, are approximately A1: 1.4 oz, A2: 1.7 oz, and A3: 0.8 oz.
3) The A1 is only about 0.6 oz heavier than the A3, and not a lot more expensive. The light is a lot brighter and the battery life is quite a bit longer.
4) The A1 is 0.3 oz lighter than the A2, and the same price. The light is a lot brighter and the battery life is longer (except on the brightest setting).
5) The A3 uses 200 Hz PWM, which causes flicker that is annoying to some people (many do not see it, or are not bothered by it). The A1 and A2 use 2.43 kHz PWM -- any flicker that causes is undetectable.
All three are good lights, and meet your requirements. The A3 is clearly the lightest, and quite adequate for most uses.
For a small trade-off (0.6 oz, $4.45) the A1 seems to me to be an interesting choice, as long as you are willing to buy into the CR123 / RCR123 battery. Here's how the A1 compares to the criteria the OP laid out in the original message (note: all that is not specific to the A1 also applies to the A2 & A3):
Now I'm looking for a trail light. I would like a light that:
-- is a headlamp
The light comes with a clip -- the manufacturer does not say you can reverse the clip so it will clip to a hat brim as a headlight, but I have found postings on the web that say you can, and Mark (above) mentioned clipping an EOS to your hat brim.
If you really do want that elastic band around your head (e.g. to use when there is no hat brim), you can get one intended to hold little lights like this one. For example, the Nite Ize Headband
-- uses rechargeable batteries (no CR2032 or whatever those are)
The A1 can take RCR123 or 16340 batteries, both of which are rechargeable. Smart chargers for them are not all that expensive. The batteries themselves are lithium ion, which means-- weighs < 1.5 oz
-- they are light, a fraction of an ounce, so carrying a spare is no big deal
-- they work well in the cold -- down to -40 -- much better than NiMH in the winter
In addition to being light weight, the A1 is very small -- 59.8mm (2.35") long x 20.4mm (0.8") diameter.
Note: for AA or AAA you can get rechargeable (NiMH) or you can get lithium batteries. You cannot, however, get AA or AAA batteries that are both lithium and rechargeable.
You can get rechargeable Li Ion batteries in those form-factors (14500 to replace AA and 10420 to replace AAA). If you use those, your light may be significantly brighter (but still not brighter than the A1).
*) The A2 description does not mention the 14500, so that is unsupported.The problem with these batteries is that they are 3.7 volts. You may be able to use them, but you need to be careful not to not let the light overheat -- especially on the brightest setting.
*) The A3 description does list the 10420, but also cautions "due to the small body size, 10420 batteries are not recommended since they may cause the light to become hot very quickly".
The A1 weighs about 1.4 oz, including the battery
In a perfect world, it'd also be able to clip to my hat
You can do that -- see above
might even have different brightness settings or a red led option.
There are three brightness settings (A1: 1.8, 35, 190 lumens; A2, A3: 1.5, 18, and 80 lumens).
There is no red LED -- you'd have to use a filter for that. OTOH you may not care -- from what I read, the 1.8 lumen setting is pretty good about preserving night vision.
but mostly, minimal, light as possible, headlamp than I can recharge batteries for.
From what I can find, this is as minimal as it gets. You have to take a battery, and the A1 battery is quite a light battery. The light itself only adds 22 grams.
OK -- the A3 version is even more minimal than the A1, but I explained above why I think the A1 would be worth the extra 0.6 oz
Reassuringly, all three versions of this light (the A1 & A3 are the most popular) have a good reputation on Candlepower Forum. Owners love them.