The POD here is that in 1980 the deadly word "co-presidency" never comes up; Ford takes Reagan's offer of the nomination for VP without anything more than the routine assurances that "*of course* you'll be consulted, *of course* you'll have an important role," etc. Now suppose Reagan is killed in 1981. (Somehow the fact of Ford rather than Bush being vice-president infinitesimally affects Hinckley's aim or Reagan's position--let's say Reagan is chuckling while recalling a Saturday Night Live skit on vice-president Ford he saw the other night, and moves a little. Anyway, you get the idea.)
Now assume that the (second) Ford administration is not too different from the first Reagan one--that Ford pretty much adheres to Reagan policies if only because as vice-president he defended them out of loyalty and feels he can't go back now, and anyway he knows that he will face a revolt by the conservative wing of the GOP if he tries to backtrack too much. As in OTL there's a recession in 1982, a loosening of credit by the Fed, and a subsequent recovery. All in all, though the Republicans lose ground in the 1982 elections, by 1984 Ford is much more popular than he had been during his first term.
Now the interesting thing is: Ford can run for--and probably win--a third term in 1984! Yes, even though he served over half a term from 1974-77 and will have been serving a nearly full term from 1981-1985. Read the 22nd Amendment closely: "No person shall be *elected* to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be *elected* to the office of President more than once." (My emphasis.) Ford did hold the office of president for more than two years in 1974-77; but he was not *elected* president either then or in 1980 and therefore, unless I am missing something, there is no constitutional reason he cannot be elected in 1984. (It will after all be his first election to the presidency!)
I suppose that he could face arguments that he is trying to get around the "spirit" of the amendment, first from conservative primary opposition in 1984 and then from Mondale or whoever else won the Democratic nomination. But with the advantage of incumbency at a time of peace and prosperity, with a sufficiently conservative record to satisfy most of the Right (which in any event would have no candidate of the stature of Reagan) and with the likely Democratic candidates all having weaknesses of their own, I would bet on Ford. (Once he is finally president in his own right--not Nixon's or Reagan's choice for vice-president who then became president--he may be less conservative than I portray him as having been in 1981-84.)
And if anyone thinks he would be too old to run in 1984, remember that he was over two years younger than Reagan...