That wrap was used in some 70s cues done by a few U.S. production houses- one of them was the H Betti company which is now known as Imperial Cues - they have been an import cue firm for a very long time now- Mr. Betti- long deceased- his great grandson runs the firm now- bought out the guy who had bought out Saul Rich ( Rich Cues - of NY not Abe Rich of Miami ( Star Cues); when it was still in NY and NJ. They assembled some cues here in the U.S for a while ., then switched to overseas.
That wrap with a weird coating was used on many of their cues, and the last cues assembled in the U.S. used woods left over from the original Rich Cue company- that may also explain why the wood was dense enough to have weight and balanced enough to feel somewhat custom.
For a while, when they first bought the company - they engraved the name H Betti on the cue butt cap. There are very few of those left- I gave the last one I found to MR. Betti's Grandson who runs Imperial now- he is a really nice guy. Mine was Rosewood with pearl inlays- 20/21 ounces and also hit very well- it was in mint condition and the Grandson did no own an H Betti cue.
My guess is that you have a later H Betti / early Imperial cue - during the transition to overseas the cues were not marked. Does it have a 5/16 18 or 5/16 14 joint? the weight bolt is also consistent with the early Imperial cues. Also- they were using those pearl dots on most of their transition cues- mine had them as well. Your cue is most probably a hybrid, using woods and parts left over from the Saul Rich era and assembled quite possibly in Asia, under H Betti/Imperial supervision. Please see my former H Betti cue here: Same WRAP.