From my experience Blennies are shy creatures. It took a long time for mine to be comfortable with me close to the tank & I have to approach slowly if he is out to avoid startling it.
When I feed my tank, the blenny gets excited & will come out but I have never seen it actually eat brine, mysis, flakes, etc. My tank has a healthy growth of pink/red coraline, green & brown algae. I only clean the front glass on my tank, the back & sides are left alone. The first week I had the LMB, I didn't clean my glass at all, just let the algae grow. I know the Blenny is eating the green & brown algae on the glass because it leaves me "blenny kisses", you can see the mouth impressions where the algae was bitten off.
Honestly, my advice would be to take it back to the LFS or trade it to someone with an established tank before it dies. If this is not possible, leave the lights on longer & don't clean your glass to encourage algae growth. While, I never thought I would say this..do a water change with a little tap water, that would encourage an algae bloom quickly.