I think i found the problem, only time will tell, yes? 1982 ford mercury brougham?

My car would start ok when cold, but when hot, it would not start. After a cooling period, it would start. I could cross the starter soliniod and it would crank, but not start. Research suggests that the coil is the problem, with all my symptoms such as… Gutless.using lots of fuel, and not starting when hot, but starting cold. Does this make sense?
Added (1). Also it would jerk when going up a hill

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