Scott, sorry I have little knowledge of your fueling system however as you deduced there is a safety system though perhaps not inertia, more along the lines that if the ECU does not detect an engine turning over/running signal then the fuel pump is denied an electrical supply. I think to detect engine turning over the system requires to detect air flow. if you have the flapper type air measurement system I think there is a switch activated within the flapper mechanism, which seems unlikely to be the issue, but it will no doubt have wiring and connectors between it and it`s input to the ECU and dependent on that input, an output from the ECU to a relay to then bring on the pump...
I suspect that whatever system you have you will find a brake-down of it`s operation at GoMoG.com, as the webmaster there has researched all sorts of EFI possibilities for Morgans.
Good luck.
