The “standard” difference between TS and TRS is not mono/stereo but rather unbalanced/balanced.
Unbalanced is fine for instruments to their amps and such. Anything else carrying a low-level audio signal will benefit from using a TSR/balanced cable to prevent outside interference, especially over longer distances (more than 2m or so). Not all gear has the option to send/receive balanced signal, in which case it makes no sense to use balanced cable and simple unbalanced/TS will do the job.
With all that said, you CAN use a TRS cable to hook up a stereo source that uses a single TRS output (highly unusual I think) to another stereo TRS input.
Most audio/PA gear I know will use Jack inputs only for single channel (i.e. mono) use. The only exception here are the FX Send/Return connectors on PA/Recording mixers that use TSR to send AND receive back a mono signal going into and back out from an outside effect unit.
So, can you use TRS cable for stereo signal yes, but it is highly unlikely you will find gear that uses that cable in that way.
The other way around now, to answer your question. Can you use TSR cable for mono signal? If you read what I said so far you will already have come to the conclusion that the way TSR cable is NORMALLY used IS for mono use, but balanced.
So your question should really be “can you use a TRS cable to make a mono UNBALANCED connection?”, for example between two pieces of gear where at least one has no balanced input or output. And the answer is yes, no problem. The R(ing) lead in the cable is simply not used.
Can you tell us what you are trying to connect to what. And why Jack? XLR is -by far- the preferred connector in PA, not in the least because it’s got a locking feature to prevent accidental disconnection.
Clearly a lot of controllers will have (balanced) Jack master/booth output for cost and/or space reasons.