To take just your second example

I wish X were here

means the same as

X is not here but I would like him to be

If there are reasons other than your personal preference for X to be present then

it would be better if X were here

would be correct.

In this case "were" has nothing to do with the past tense of "to be" but is the Subjunctive mood - https://en.wikipedia.org/wiki/Subjunctive_mood#English

"Were" for the subjunctive has largely been replaced in (British) English in favour of "was".

I wish X was here

To take just your second example

I wish X were here

means the same as

X is not here but I would like him to be

If there are reasons other than your personal preference for X to be present then

it would be better if X were here

would be correct.

In this case "were" has nothing to do with the past tense of "to be" but is the Subjunctive mood - https://en.wikipedia.org/wiki/Subjunctive_mood#English

"Were" for the subjunctive has largely been replaced in English in favour of "was".

I wish X was here

To take just your second example

I wish X were here

means the same as

X is not here but I would like him to be

If there are reasons other than your personal preference for X to be present then

it would be better if X were here

would be correct.

In this case "were" has nothing to do with the past tense of "to be" but is the Subjunctive mood - https://en.wikipedia.org/wiki/Subjunctive_mood#English

'Correct' use of the subjunctive is becoming less common in (British) English in favour of "was".

I wish X was here

It's currently unclear how accepted this usage is.

To take just your second example

I wish X were here

means the same as

X is not here but I would like him to be

If there are reasons other than your personal preference for X to be present then

it would be better if X were here

would be correct.

In this case "were" has nothing to do with the past tense of "to be" but is the Subjunctive mood - https://en.wikipedia.org/wiki/Subjunctive_mood#English

"Were" for the subjunctive has largely been replaced in (British) English in favour of "was".

I wish X was here