What bulb are you using with a 10440?
That's a good question. They were produced by Lamptronix
for use in avionics in Teen Series combat aircraft (Tomcat, Eagle, Hornet, etc.). I found some surplus on eBay wow 5 years ago, assuming incorrectly they were MiniMag replacement lamps. The MiniMag lamps will flash on Li-ion, but they work well with a single LiFePO4, and are brighter than the Lamptronix, which are yellow, and dim over time from carbon building up on the inside of the bulb. But they sure are durable, and while they're bright, the color temperature is very nice if you like incan.
Thing is the reflector and lens will melt. That's why I drilled a hole in my lens. But I have hope there's an Al OP reflector
that might be able to work in a Soli head, and with some kind of modification, maybe tiny washers stacked and glued on the bottom, maybe it can activate the Soli switch. Glass lenses can be found, though usually massively convex in that size, with which I am fine. The difficulty is in making the lens work as, according to bykfixer (ty), the plastic lens is press fit, so after figuring out how to get the plastic lens out, technically the easy part though it isn't easy, there will be more difficulty in installing the glass lens.
I have also crammed a Mag-Num Star 3 cell bipin
in a Solitaire, which will work with bent pins and widening the reflector hole, and removing the lens, but the plastic reflector is no longer doing anything other than activating the switch (so pure incan flood). What's left of the reflector will continue to melt with every use until the lamp is permanently stuck in the reflector, pins pull out of the socket, making it near impossible to seat the pins back in the socket (because the head screws on and off). But it was fun while it lasted.