Which LED Module To Replace PR16 Bulb?

I just bought the Burnham Brothers scope-mounted shooting light for my .22 rifle. It's not the brightest or most sophisticated of lights, but it's good enough to deal with the varmints that raid my vegetable garden nightly (I'm in Florida, this is the growing season).
My biggest problem is the shockingly short battery life. It uses two 9-volts, and if the light were left on, they would last less than ten minutes.
Would replacing the bulb with an LED module extend battery life? If so, which module should I buy? Any advice would be appreciated.

advise?
skip the whole light!
bulb, batteries, ..., everything is a very less than ideal base

but that PR16 is a totally normal thing, if You really want, get any of the led-inserts for that holder. f.e. the led inserts for Mags C and D cell lights

(personally I think any modern 2 AA or 2 CR123 led-light will be much better + offers more runtime. In that runtime class, even a single AA led-light that houses an 14500 Li-Ion cell will kick the scope mounted one)