I saw a custom M98 for sale that listed a "side stalking safety" in addition to the regular safety. What is that and why would anybody want one?

Don't know for sure, but I assume it is a trigger-block safety that would be used when still-hunting (stalking) as it would arguably be faster to operate than the bolt safety. I wouldn't want one.

Sometimes that term refers to the "greener" style that goes thru the wrist of the stock. It is often used on doubles, but can be used on bolt rifles to the block the kicker on double set triggers.

It is usually used to quickly render the rifle safe when it might be too noisy to engage the wing safety. Also used when a low scope prevents the wing safety from being engaged.

Of course, it could mean a Timney side safety.

They were semi-popular on German guns. By nature, the German gunmakers loved engineering, redundancy, and things for technology's sake. This extra safety fit all three bills. The ones I have seen were all in conjunction with a function wing safety that worked under high mounted scopes. It was an extra mechanical doo-dad that the Germans could not resist adding at times.