There should be a plate just rear of the door handle that indicates the length and serial number of the TT (there are members that can tell you the year the trailer was made by the serial number). I can see that it's there in your picture. Most trailer lengths (if measuring with a tape) include the length of the tongue.
With this, you can post on the forums and someone with a similar coach will have an owners manual, and be able to tell you how much is weights.
From that you should be able to take the owners manual of your s10 and determine it's maximum towing weight.
Off hand, from your picture, I would guess your TT was built in the late 50's and about 19-20 feet in length. I would think you need at least a 4+ liter engine (understand that I live and tow up and down mountains, which requires more power)... but that's all based on a guess of your trailer and it's respective weight.
Hope that helps a little,
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