About gifts in a jar, how long will one 'keep' @ room temp with parmesan cheese in the ingredients?

Parmesan cheese actually doesn't need to be refrigerated. Once I asked a lady in a cheese shop if she had any ice to keep it cold while I drove for an hour and she told me 'there was cheese way before there were ice cubes.'

If you use real Parma-Reggiano just keep it cool and in a dark place and it will keep a long time.

However you are mixing it with other ingredients that will go bad if they absorb some of the moisture from the cheese. I would keep the mix in the fridge. If you want to eat it at room temperature just let it sit out for 1/2 and hour before chomping.

I read somewhere that Parmesan, may be stored at “room temperature” for significant periods of time if kept moist....I have stored it at room temp in the winter for a few days...

A few days