Hi,
Never worked on one of these....
....so....if I'm not spot on, just know that I'm only trying to help and taking my best guess.
Was it overheating? Or did you replace the pump simply because the tell-tale stream was weak?
If it's not overheating and it's just the tell-tale is weak, I would look into the 25 year old plumbing components which, if my guess is close, are (maybe) items
3, 23, 24, 28, 47 and 51 in the link below.
I list those items because they all seem to be located in the forward right corner of the lower case and that's near where the water check (tell-tale) fitting is located. Item 41 in the link below:
I would start with making sure the water check fitting is clear and then just start examining each of those components, one by one as you move away from the fitting making sure they are clear and unobstructed. After 1/4 of a century, those hoses and "T" joints may have deposits or debris inside them.
There are other components that may need checking as well, like, possibly, items 25 and 26 in the first link above. I don't know. But, if it were mine, I would want to know those were clear too as that appears to be the fuel cooler.
Another area that has me wondering is what looks to be an oil cooler of sorts in the engine block. That looks like an area that could trap sand and debris. There's also a sacrificial anode (item 3) in there that might need replacement. The cover is item 15 in the link below.
If there's access room, I would want to inspect in there and replace the anode and screw while the gasket and parts are still available. If you plan on keeping and running her some more years I consider that worth doing if possible. Note that there are two more anodes and screws on the opposite side of the block. Always replace the mounting screw with the anode on a Honda.
I see other things, albeit not related to your current issue, that I would want to check and keep "fit" while parts were still obtainable. But, I'm just an old, fat, armchair quarterback making assumptions about someone else's gear. The old "if it ain't broke, don't fix it" is often very accurate and relevant to stuff like this. And anyway, I'm definitely not sure if any of my ramblings so far are of any help to you or not.
I had never really looked at one of these before but it's obviously one of the very first fuel injected Honda outboards.
The fact that it's lasted this long speaks volumes to me about the quality that was built in.
However, all the curved hoses and "T" joints in this plumbing is inefficient and a sure invitation to small things getting stuck as they navigate through. Especially as the hoses age and harden.
Good luck with the old gal.