I'm working through lessons 54, 55, & 56 of Progress in Irish. I notice that they don't list a passive/impersonal conjugation for téigh. It would be kind of an odd construct in English ("It is gone", "It was gone", "It will be gone"??!).

Maybe there is no such thing for this verb?

There is. Go to http://www.csis.ul.ie/focloir/ agus scríobh "téigh" sa bhosca.

Don't confuse it with the other verb called "téigh".

There's the first "téigh" that means "go", and there's the second "téígh" that means "heat" -- but they've totally different forms:

He heated the water.
Théigh sé an t-uisce.

He went home.
Chuaigh sé abhaile.

I think both are spelled téigh (not téígh), but the one that means "to heat" is regular, while the one that means "to go" is irregular.

The "briathar saor" of "to go" is téitear in the present habitual (one goes), chuathas in the past, etc. Of course, there are some different forms according to the dialects.

Wouldn’t the most natural way of saying
"It is gone", "It was gone", "It will be gone" be
Tá sé imithe. Bhí sé imithe. Beidh sé imithe.
?

and don't confuse "it is gone" and "it will be gone" with "it went" "it will go"

"Someone goes, someone went," etc. an chiall atá le "téitear, chuathas" agus mar sin de. Using the briathar saor, the subject is left deliberately unspecified. It's popular in bureaucratese:

Chuathas i gcomhairle le saineolaithe. = Someone went into council with experts. = Experts were consulted. (This instead of saying "Chuaigh muid i gcomhairle le saineolaithe.")

"Using the briathar saor, the subject is left deliberately unspecified. It's popular in bureaucratese"

And when an auidit of said beuros is done to ascertain spending wastes abd corruption, the briathar náid comes into play, 'nobody spent, nobody did'