The Supra is a great boat.  I think you’ll love it.  And you can stay around here, the Supra/Moomba boards are pretty well dead.  

Aside from the larger gauge black and orange pod and ground, are those smaller gauge wires a red and a dark blue? One of those is a sense wire (likely the red), it should read exactly battery voltage.  If it doesn’t, you need to do voltage drop tests between that wire (disconnected from the alternator) and the battery.  
 

https://www.delcoremy.com/the-latest/2017/january/tech-tip-remote-sense-operation-and-system-testin

If it has an exciter wire, it will have 12 volts at key on.  
 

Alternators typically have some sort of labeling on or near the terminals, S for sense, + for positive, E for exciter, so you may need to look at it or take a picture.  
Doesn’t look like it’s that expensive of an alternator if you just throw one on too, i just like to condemn the part and replace the component instead of a whole assembly if I can.  

6 hours ago, Northwoods2024 said:

Typically only 5-8 people at a time. Have a pontoon as well so will only be using this boat for watersports. Our lake is ~250acre with max depth of 20ish feet so would likely try to do 20'. Skiing experience is intermediate, but surfing experience is beginner at best. I can get up but cant drop rope. Want to introduce surfing to my dad as it'll be easier on his body at 58 than slalom skiing is. 

Consider the depth needed to surf and ensure you have it before spending money and being disappointed.  Ie dont expect a quality wave in less than 15' of water, not sure how much of your lake that eliminates.

They look good with a tower too and a red bow cover, here's a pic of mine before we removed the tower:

I don’t know the LT4 well, but I’d start with checking the lines for the remote oil filter, the oil filter cap, and try to trace any other lines to see if there is an oil cooler or anything.