The mechanic may be correct. Have you ever replaced the fuel filter? $15 and easy to do. If the filter gets hard to push gasoline through, the pump has to work harder. If the pump works harder, it gets hot and will shut off.
Having low levels of gasoline in the tank means the pump is no longer submerged by cool gasoline and it can warm up, making it less efficient.

Replacing the pump is quite easy, just lift up the rear floor boards, remove the access panel, and replace the pump. No jack, no dropping tank, etc.
replacing the fuel filter is very easy also.

Klaus
--
The 164 has a new home, all I am left with are a 95 854T and a 98 V70R :)