Could this bee the wheel itself bar tape or more to the point the wheel itself.
It will not be the bar tape! If the punctures were on the outside (ie away from the rim side) of the tube it's definitely not the wheel. Same place points to same cause.
It could be the inner base of the rim (see below). Rim tape is the easy solution if so.
Otherwise, except if there is sharp roughness (mitigation: file and emery paper) at the valve hole, I can't see how it could be the wheel itself: no part of the wheel is otherwise touching the tube.
I assume you have the pumped up properly and assume the punctures are not 'doubles'. You haven't said you've used a new inner tube, but I assume you have (at least one).
I recommend decent rim tape prophylactically, bit like new cable outers, as part of the 'restoration' process. I've just replaced a cheaper narrower plastic tape with a 'bomb proof' Schwalbe wider thicker one (came in light blue and was 16mm (I think - am not going to take a tyre off!)). LBS charged me £2 for it. I had a slow puncture (ie could pump up and carry on for 50km). Crossed a ford - on stepping stones - and could see bubbles coming out of the valve hole so knew it was definitely a puncture. On examination (in a sink was a minute hole on the inside of the tube. No obvious cause, but old rim tape, with the spoke access holes (rim was 2x skin) really 'dimpled'. A further 250km done without repuncture, fingers crossed.
