Yes that is correct, the MFI relay is basically two relays in one housing. You should get one click when key turned to ON (run) position, then there should be a second click when key turned to start position (sometimes hard to hear with engine turning). The click you hear 5-10 seconds after key tuned to off, is fuel pump half of relay opening.
To explain operation first click (key on) is power delivery side of relay closing, that supplies many control items like IAC, fuel injectors, crank/cam sensors, air flow sensors, additional supply to couple ECU pins and possibly more items. That is for engine to be ready to start when cranked.
The second click (key start position) is to activate fuel pump side of relay, which will continue to run if engine actually starts, but if engine doesn’t start in given period of time ECU will shut pump down, it will do same thing if engine shuts off unexpected. That’s similar to you turning key off and few second delay you hear the click being when pump half of MFI opens.
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