No, it should keep counting.
Describe the problems you are having.
Chevrolet does not use a resettable fuel relay (inertia switch), that's a Ford thing.
It doesn't have a reset button.
The 99 Chevy S10 does not have a fuel pump reset button. The pump is controlled by the relay unit.
The abs light is on because there is a problem with the system. Until the problem is fixed it will remain on. Once it is fixed the light will reset itself.
Gm does not use reset/inertia switches.
It doesn't have a reset switch.
check your answer
Yes
There is no "reset" switch for the fuel pump on that vehicle.
take the negative cable off your battery and wait half hour and reattach if it comes back on better get the codes read.