Pappy said:
Try the water pump.......! When you get it apart look at the cup for grooves at the top and the bottom plate for grooves as well. If you can feel the grooves with a fingernail replace the complete pump assembly. Know that's more expensive but alot cheaper than a powerhead!
You're apparently in salt or brackish water so you may also have the grommets at the top of the water tube melted and blocking flow or corrosion build-up behind them and pushing them shut. The vintage engine you have is prone to this. Would be enough water for the telltale but not able to pump enough volume to cool the engine on plane or higher. You must pull the powerhead to replace those. Not a hard job and all you will need are two grommets and a base gasket. Good time to do the pump and all the fuel lines at the same time.
Spin fisher,
1) you checked the water jackets and cleared them....great
2) you checked the thermostat...great
3) please take Pappy's advice and evaluate the water pump, cup and housing...if you haven't done so
4) the water tube grommet that pappy was referring to is at the top of the water tube at the base of the powerhead. Those have known to become distorderd and swollen to prevent good flow of water up or even block water flow to the power head dispite a good functioning water pump. If I am not mistaken, you will still get a stream of water coming from the indicator even though there is no flow going to the head. The water indicator only tells you the water pump is working not that it flowing through the head and around the water jackets!!
You will need to remove the powerhead and inspect the grommet at the base of the powerhead. Here is a YouTube video of a 9.9hp evinrude...basically same motor different Hp. It make a good reference to the upper water tube grommet at the base of the power head.
https://www.youtube.com/user/cpgixxer#p/u/65/cqYiFl6I_20
I hope this helps...good luck!