Hey falcon, I can have a look at my same water pump on the shelf tonight and get back to you, seeing his is now in. It’s the standard 3sgte style impeller, not the once off design of the stxxx Celica pump (the one that’s different to all other gens - said to be better but no data to back up why) style. If you need to improve coolant flow / temps, IMO change water pump as per major device (including the back housing) and only run the high flow lower temp thermostat (available for both gens through ATS racing and other suppliers).
Cogs.
Oil pumps 5sfe = gen 3 = gen 4, all have 25 teeth cogs resulting in a gen 3 timing belt needed. Gen 2 oil pump cog has 27 teeth. Based on the cog dictates the timing belt needed.
Pumps.
The late model 5sfe oil pump can be used on a gen 2 3sgte, matching the block and sump (not cog). It is a common upgrade and IMO should be done for all gen2 owners. Late model 5s oil pump has a deeper 15.x mm gator instead of the gen2/3 13.x gator. The gen3 used a smaller cog to up the speed of the pump to combat the prior issue. The gen4/5 has a 15.x gator and small cog however can not be used with a gen 2/3 due to not matching the sumps.
If you don’t get the above right with the cog / tensioner / timing belt etc, often the camshaft timing will skipping a tooth because of low tension on the timing belt.
Oil relief valves are stock in above.
ATS Racing does a custom late model 5s oil pump 15.x gator for gen 2, with the correct pulley as well as the relief valve modification.