That's not a water ski tow unit, it doesn't have the horsepower or enough thrust for that. It's a tow unit for a snorkeler to be pulled in the water while surfing his body. That's why it has the hold bars at the back of it. I'm trying to find it on the web now. I've seen it, but can't remember where. I'd say it's from about 1967.
Here's one that sold on Ebay for $200 a couple months ago. I hope the seller doesn't mind I downloaded his photos, since the auction listing will probably vanish shortly:
VINTAGE WATER SCOOTER JET SKI WATER CRAFT | eBay
Quote the seller:
"TO ALL: I do not know what this is, when it was made or where it was made. It has no numbers or name on it anywhere other than the engine. ALSO I WILL BE UNAVAILABLE FROM FEB 8 TO FEB 16 FOR EMAILS SHIPPING ETC.. This unit is fiberglass, about 4 foot long and 28 inches high. I would guess weight at about 50lbs. It is powered by a small Tecumseh engine (inboard) . I think it has a centrifical clutch beneath the engine but i am not sure. It is missing the top cover which appears to be of simple design and easily fabricated. It exhaust at the top, I assume there was a hole in the top cover for the exhaust. I did run fuel into the engine from a temporary gas tank and it started easily and ran fine but i did not run it for a long time. I did not want to put gas in the inboard fiberglass tank due to shipping concerns. The prop turned when the engine ran so i assume everything works. To use this you put it in the water and it pulls you. The bar on the back is the throttle and there is a wire coming out for the choke. I will ship this at actual shipping cost no matter what is listed. Cost will include any packaging that i have to purchase. If anyone knows anything about this i would appreciate the info. Unit has been in my dusty shop for about 6 months. Paint is fair, A lot of what you see in the picture is dust that will clean up."
Here is his contact info, maybe he knows more now. Please don't abuse it.
eBay Feedback Profile for jamie_julie