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I'm still somewhat confused regarding the subjunctive mood. Suppose we are talking about two different people, two "hes", is this correct?

(1) He is rich, and he wishes he were rich.

(2) He was rich, and he wishes he were rich. (or "he wishes he had been rich"?)

(3) He has been rich, and he wishes he had been rich.

(4) He had been rich, and he wishes he had been rich.

Does it work like this: we take the same form of the verb and move it to the past tense if it is in the future tense and then take the subjunctive form? So in (1) we go from simple present to subjunctive simple past, in (2) from simple past to subjunctive simple past, in (3) from present perfect to subjunctive past perfect, and in (4) from past perfect to subjunctive past perfect?

What about the past tense forms; do we leave these in the past, or do we move them back further, for example to a past perfect as shown in brackets in (2)? If so, what about (4)?
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You have confused me thoroughly with your two 'he's'. What is the point of causing purposeful confusion?
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The grammar of wish is unique. I would not recommend applying the grammatical patterns used with wish in cases where a different verb is used.

As for backshifting, it's used all over the place, not only with wish, hope, believe, and not only when a situation is untrue or unlikely.

I think he's intelligent.
I thought he was intelligent.
I know she's happy.
I knew she was happy.
I am certain that he is leaving tomorrow.
I was certain that he was leaving the next day.
Lucy is sure that Robert has gone.

Lucy was sure that Robert had gone.
She insists that she has seen the two of them together.
She insisted that she had seen the two of them together.
They state unequivocally that the plane will arrive at 10.
They stated unequivocally that the plane would arrive at 10.

CJ
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I just wanted to keep the two parts before and after the comma as similar as possible. I probably should've used Alice and Bob, but I didn't think of that when posting.

(1) Alice is rich, and Bob wishes he were rich.

(2) Alice was rich, and Bob wishes he were rich. (or "Bob wishes he had been rich"?)

(3) Alice has been rich, and Bob wishes he had been rich.

(4) Alice had been rich, and Bob wishes he had been rich.
I see.

(1) Alice is rich, and Bob wishes he were rich.
(2) Alice was rich, and Bob wishes he had been rich.
(3) Alice has been rich, and Bob wishes he had been rich.
(4) Alice had been rich, and Bob wishes he had been rich.
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OK. So this is equivalent to reported speech where there is a backshift in tense (except that here you use the subjunctive instead of indicative form)?

And this is only used when you wish (or hope, believe, etc.) that something were true which, in fact, it is not (or highly unlikely)? The backshift, I mean, not the subjunctive in general.
 CalifJim's reply was promoted to an answer.