You're right that shrimp don't carry their eggs under the tail until they are fertilized.
If you're willing to keep it, then it might pair with a watchman or a wheeler or some other shrimp goby that you like, or can find wherever you get fish.
I'm not sure if a solo pistol will build a burrow the way they do when paired with a goby, do they just bury themselves and hide? If the tank bottom is visible from the underside, there's a chance you'll be able to see it from underneath.
If you're willing to replenish your cleanup crew periodically, they're great to watch, and the fish might keep the shrimp fed so it will kill less, but it will still kill anything that wanders into the burrow. I regularly find empty shells at the burrow entrance, and any time I've tried an emerald crab, it winds up a dead carcass on their doorstep.
That looks like a bullseye pistol.
