How to clean A. D. Leveridge Gauge?

Tips on cleaning this? I’ve been told WD40, also told Mineral Oil (which seems like a bad idea)

Suggestions?

Should I just bring it to my watch guy for a cleaning?

It’s a good gauge and worth spending some money on, to have your watch guy clean it with an appropriate solvent and then lubricate it with a light oil which he will be able to apply very precisely.
I wouldn’t think of doing such a thing myself when I know it will probably be done better and last longer when someone more skilled can do it with chemicals I would have to buy and have no other use for.
Doubtless others have a different opinion but if you already know a guy and trust him, why not use him?

Thanks, it’s older than I am so probably best to spend $100 on cleaning than mess it up myself.