I think any 18650 light is going to be pretty heavy to put on a hat. Maybe consider AAA?
Not at all if you have the right light. I can keep my little Olight on my cap for two hours working on equipment in the dark and I’ll forget its there until I lift my head and inadvertently blind one of my co-workers.
Here’s a pro tip - drop Olight a line in Atlanta (the ‘contact us’ thingy is on their website); I’ve found them to be amazingly accommodating on warranty. Unless you ran over it with a D6 Cat, there’s a good chance they’ll give it an overhaul and send it back as good as new.
When I had a problem, I literally had an email response within the hour. I was very impressed with them.
I highly recommend the Utorch Ut-01. with a 14500 battery, it’s around 800 lumens and will run on AA batteries at around 400 lumens. With a coupon code you can get it for $10!
Second, if you wanted an 18650 light, the Jetbeam E40 is pretty small and light. It’s 1100 lumens and cost with a code is $36.
Yup, that is the smallest/shortest 18650 light I know, and even then, while I did use to walk with it attached to the brim of my hat, you can definitely feel its weight, which makes it problematic.
Nowadays I walk around with either UT-01 or OTR M3.
Why don’t you fix your light?
Replace the driver and emitter?
If there may come a time I can’t order a new Convoy S2+ I’l fix it :).
Astrolux E02 should do you good. $21.53 at FastTech.
https://www.fasttech.com/product/7028901-astrolux-e02-led-flashlight
The lightest 18650 light that I own is skillhunt h03 (angle light).
No chance of talking you into an actual headlight? Not to crow about it again, but the RJ02 is dirt-cheap, you can replace the TIRs from spotlight to wide-angle in a minute or less, and it gets pretty good runtime.
With a 60° TIR, it’s perfect for me, nice’n’floody.
Plus, you can swivel it up/down with those nice rubbery rings (ie, no discrete hinge that can break oh so easily) so you don’t have to constantly crane your head in the preferred direction.
Just today a thread has started about a new light that fits your requirement, the Ultratac S20
The way the clip is placed, when you reverse it, I think it will make it difficult to carry on the brim of a hat. It will be sticking pretty far out, thus making its weight more noticeable.
After considering the possibilities, I think I’ll look for a good price for the On The Road M6. It is remarkably similar to my old light with almost twice the lumens. At the same time, I’ll contact Olight and see what they say about fixing my old S20R. Thanks for all the input, folks. What did I ever do without you guys? 
Seems like an appropriate place to tout my fave EDC 18650 light - Nitecore HC30.
Same claimed lumens as the OTR (so probably more in reality).
Shorter.
Lighter.
More throw, yet still has 100 deg beam (ie decent flood).
1 lumen low (vs 10 for OTR)
Great headband.
Removable clip.
Great mode spacing.
CW/NW options.
Available for around $35 with coupon.
In general I’d expect quality to be a notch above OTR.
nothing beats the EMISAR D4 for price output size UI… might want to buy that…
If you don’t have a headlamp I’d buy the skillhuint h03 for like 30$
The OTR M6 is very similar to the Olight S20 (like your S20R without the charging dock feature) but it’s definitely not off the same assembly line. I have both and although similar there are very slight differences.
The successor to the S20 is the S2, and it has nearly double the output. (950lm vs 550lm)
There’s two currently on ebay, the first one (if no one else bids) will cost you $33.59
The second one has one bid, currently at $27.49 shipped.
https://www.ebay.com/itm/olight-s2-baton/222889443686?hash=item33e53f0166:g:pRQAAOSwOy1arzx7
https://www.ebay.com/itm/Olight-S2-BATON/222889477058?hash=item33e53f83c2:g:eIQAAOSw2CJar0gC
.
Or why not just buy an OTR M6, it’s under your $30 budget:
Gearbest:
(1A) $28.45 with code GB2017LED (Dispatch: Mar 21 - Mar 23) https://www.gearbest.com/led-flashlights/pp_423440.html?wid=21
(5C) $29.84 with code GB2017LED (Dispatch: Apr 2 - Apr 6 ) https://www.gearbest.com/led-flashlights/pp_423441.html?wid=21
The 5C was on sale for $25.00 but just ended yesterday (I replied to you about that in this thread: ☢ [Bilakos10 Premium Deals] ● Astrolux FT03 SST-40 ● Astrolux A01 UV ● Seeknite X6S ● JCD 8898 Hot Air Station ● SQ-D60 - #2160 by beam0 )
Also in stock at Fasttech:
Complete kit w/ charger and 2600mAh battery, (1A CW version) $31.38 shipped w/code BLF for 5% off: https://www.fasttech.com/products/4206301
Unfortunately just missed the Fasttech St.Patrick’s Day Sale for 10% off Site-wide (ended 3 days ago)
The 3C NW version is discontinued at Gearbest and I can’t find it anywhere else.
The OTR M6 is also sold on AliExpress on OTR official store!
Within 1 week there will be a sale and maybe you can get it with a nice discount if you opt for that light 
BTW, the OTR store has new lights as well
https://ontheroad.aliexpress.com/store/3081046?spm=2114.10010108.0.0.780220bfWoR3Vi
Thanks for this! I slightly remember seeing this store one time but totally forgot it!
When the sale begins M6 will be only $22.95 - $23.95… but they add shipping charge ($4.55) So $27.50-$28.50 total, still not bad!
Thanks for keeping me in mind. I think I’ll be jumping on one of these deals. :+1:
Skillhunt H03 is the one I would recommend for small 18650 light. I don’t use it as headlamp.