Velocity XL pilot reported a fuel reading issue and fuel pressure warning during descent. The engine began to sputter prompting the pilot to divert to the nearest airport. Post flight inspection revealed an old fuel cap poorly seated was a possible contributing factor.

Narrative

During cruise one tank was consuming fuel faster than the other even [though] they are interconnected. Right tank reading empty; but there was almost over an hour in the left tank. Cruise on left tank was sufficient for nearly 15 minutes. During last part of descent into ZZZ; engine sputtered and fuel pressure warning occurred (even though there was still almost 1 hour of fuel in left tank). Fuel boost pump on low seemed to resolve the issue but because I wasn't sure if the engine would stay on at idle throttle settings; and because ZZZ1 was directly in front of me with a large runway; I chose to divert there. Because it is a PPR (Prior Permission Required) airport the only way to get that diversion was to request priority handling (which given the night conditions I sure felt it was appropriate). Landing was without incident; but turning off the boost pump on the ground resulted in sputtering engine. After talking with my local A&P; and a fuel system inspection; he believes the root of the unbalanced fuel consumption was a poorly seated; and older fuel cap. It has since been replaced with new fuel caps.In general I was happy with my decision making during the event; although it may have been a bit overly conservative since the boost pump resolved the issue. In hindsight; it may have been prudent to divert earlier when I noticed the unbalanced fuel consumption between the tanks. I believe with the inspection from my A&P; and the testing of the fuel system (including venting and caps); this issue should be resolved.