That is the correct routing.

Ya I was backwards, I run two stage pumps been a while since I ran a bravo

"A project boat with no history" = install new sea pump impeller kits

Have you verified that water is getting to the pump? Could be a bad case of bravoitis. The hose gets collapsed from corrosion where it goes into the transom assembly.
If it gets to the pump and it's plummed correctly then see if water is coming thru the oil cooler. If not the cooler could be full of impeller pieces or the impeller itself in bad shape.

when you turn the hose on full it will be blowing out around the muffs. if the impeller is pumping that water will all get sucked up and quit blowing out. you can tell when it is sucking water and when it is not. as said they move a ton of water, way more than the hose will supply

Update, Good call Griff. When I got the second motor up and running it had water coming out of the exhaust. I bought two replacement kits and did both engines. Glad I did.

• Check your coolers. You have broken impellers.

Ya, Id back flush them to make sure no bits are down stream from the pump

Back flush from thermostat water inlet hose, remove the output hose from the raw water pump to clean any broken veins from the impellers stuck in the coolers or you will have future problems.

THANKS for the excellent advice everyone, I’ll get on that this week.