On the wood versions I don't know where you would find the serial number. Many "non-Thompson-Chris-Craft" boats used the brass plaque but often those come up missing. On a cruiser they would stamp in the serial number on the bottom of the cabin drawers and on things like the back edge of the hatch cover leading from helm to cabin. You may have to look carefully around to find something, but good luck. I don't know how Thompson-by-Chris-Craft numbered the boats, and apparently neither did Jerry Conrad because these boats don't even show up in the ESSENTIAL GUIDE book published by the Mariners Museum. Look up under the front deck on the inner side of the bow, or under the engine hatch, anywhere if you can find a series of numbers that would be great. I even found a serial number in pencil, scrawled out on the inside of my 1966 38 Commander Express electrical cabinet, that matched the other numbers I found around inside the boat (which was the way CC was able to build components in other locations and have them properly brought together for the proper boat.
Your particular boat is a rare one. Don't under-estimate the collector value or significance of this particular boat because I suspect there were relatively few built and far less surviving today in any kind of operable condition. I like the design, sort of a modernized Sea Skiff concept for Chris-Craft at the time. The boat could be 1963 instead of 1968
With Eaton outdrive and small block ford power, you have something that may actually belong in a museum somewhere !! Very cool.