One option is a non-absorbent tape like Benotto Cellotape. It has no cushion (not like you need it indoors), just grip; but it was standard issue for pro cycling teams in the 80s.

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ECMGN Therapy Silicon Valley:
Depression, Neurocognitive problems, Dementias (Testing and Evaluation), Trauma and PTSD, Traumatic Brain Injury (TBI)

Ummm, wash it from time to time? Just an idea.....

That photo is so good.

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http://www.jt10000.com/

With soapy water? I've never washed handlebar tape, but maybe I should start.

Get a few of those scented car hanging trees. Next time you put on fresh bar tape, just wrap the trees underneath. Provides a pine fresh sent, and also gives more comfort padding!

I have had some kinds of synthetic tape that wrap tight and somehow allow sweat to get trapped under the tape. In that case no amount of washing the surface helps. Change your tape you may find a nasty wet bar underneath.

You can actually throw it in the wash and it comes out like brand new.

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''Sweeney - you can both crush your AG *and* cruise in dead last!! 😂 '' Murphy's Law

And Schwinn Collegiates, Varsities and Continentals. Color-matched to the frame.
Yes I'm old...

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Brian

Gonna buy a fast car, put on my lead boots, take a long, long drive
I may end up spending all my money, but I'll still be alive

Or you may find something even uglier underneath.

Shortly before Xmas, I was cycling at about 25 mph when I rode over a small bump with the change of the road surface and my handlebars snapped. I was fortunate my broken handlebar didn't go through my front wheel and I was able to bring the bike to a controlled stop.

When the tape was removed it revealed the handlebars were heavily corroded from sweat and riddled with large holes. It was surprising it didn't break earlier than it had.

I still think back to a couple of miles earlier when I descended a hill with sweeping bends where I usually max 40 to 45 mph. I'll be removing my tape and checking my bars annually from now on.

What material were your bars made from? Aluminium or carbon fibre? I've had a set of aluminium bars snap on me due to metal fatigue (I was less fortunate than you, had a fairly nasty crash), but other than the crack they weren't at all corroded.