Yep. Yellowish grey with stripes definitely sounds like he is stressed. I would give it some more time before putting the goby in a different tank. That is very odd that you purchased them together but now they will not share the same burrow. Do you have actinics, or a way to reduce the amount of light in the tank. When I add new fish to the tank I usually will only leave the actinics on to help ease the stress on the fish.
That still doesn't explain why he is stressed. Could there possibly be another critter living in the burrow with the pistol shrimp, like a crab or a mantis? I would turn the lights down and give it a couple of days. If the situation does not improve then moving him to another tank might be the best option, even though it would endure more stress. It is a tough one to call. Try to evaluate any and every reason as to what is causing the stress. Good luck.
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