What I’m asking is is there any such thing as a “16 ohm output”?

Yep, and rather common.

Transformer are wound to a ratio.

So changing the impedance on one side

is reflected on the other.

Aside from losses the impedance is not set.

The ratio is. change one side the other side changes too

according to the winding ratio.

Current is more a issue, so trying to make a 4 ohms tap

2 ohms is possible.

But 2 ohms is very high current so usually more

thicker wire is needed

Far as using 8 ohm tap as 16 ohms.

16 ohms less current so wont be issue.

You just have to calculate the ratio

to see what the primary / tubes will see

if you running different load on secondary.

basic math if you doubling or halving the load.

incredible basic common guitar transformer.

8 ohm output tap, and primary would be 3k

4 ohm load, primary be 1.5 K

8 ohm load , primary be 3 K

16 ohm load, primary be 6 K

impedance not set, the ratio is.

as mentioned a 4 ohm load = more current.

so usually the winding be designed to handle

more current.

So better idea to change 8 ohm tap to 16 ohm.

Why many many old Fenders where just a 4 ohm

output. The windings where designed for biggest load.

No problem to run 8 ohm or 4 ohm load.

Of course the primary changed.

common 6L6 pair for Fenders.

6L6 pair does fine on 3.3 to 6.8K

least for Guitar bandwidth/ distortion levels.

So weasel cheap transformer be 3.3k primary 4 ohm tap

be fine with 8 or 4 ohm load.

Of course there is plenty of after markets with multiple taps.

Easiest off the shelf transformer is " Marshall " style

should have 16 , 8 and 4 ohm taps

or just a dual tap transformer. with 8 and 4 ohms.

You could use 8 ohms as 16 ohm. and 4 ohm as 8 ohm.