I think the age 60 rule only applies to part 121. After that, if you can still hold a medical, you can do any flying other than 121. I think a there are a few guys over 60 flying 135. The chief pilot at an old flight school of mine was 86!
There's currently another over 60 limitation...you can't fly as PIC anywhere out of the country on any commercial flight. That means Part 121 or 135, scheduled or unscheduled.
The rule is an ICAO rule. I can quote if if anyone cares. ICAO has made some noises about voting to amend the age to 65 but that hasn't happened yet.
In the real world, most 135 operators don't pay any attention to the ICAO rule because few, if any, of the member states care or enforce it. But I know of at least one operator that takes the rule at face value and there may be others.