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Hi and Welcome to Just Answer! EFI relay coil is grounded permanently on one side and it is activated from engine computer when car is running. the reasonfor relay coil to to osculate fast when key is off is small power feedback to the activation side of the coil. power is very weak but enough to trigger the relay but when coil clicks and put load it is not enough to hold and spring pulls back the anchor, then it all repeats.
It will be impossible for me from this forum to point to where the short is or where the feedback is coming from. it could be corroded connector. check lower left footwell area on driver side. open and inspect all connectors close to the floor.
The wire coming for relay control from ECM is blue with orange stripe and it starts at connector E8 cavity #8
to identify this connector use wire colors. and they are as follows
1-black-red 2 black orange 3- breen black 4- white 5-empty
6-blackorange 7-black red 8-blue orange 9-green orange
10- green 11 empty 12 empty 13 -brown 14- violet 15- redblue or green white 16- black and white 17- pink 18- empty 19-empty 20- white green 21-gray 22- violet white