I was checking for leaks and noticed the rubber screen trim was not as tight onto the scuttle in the middle as towards the sides. Probably a mis-match in the curvatures of the scuttle and screen frame. Hand made tolerances! Whilst cleaning in readiness to put some sealer under the rubber I spotted a wire under the screen frame rubber. It had been stuck there during screen fitting probably from new. A prime situation to cause a wire failure/short. I wasn’t having any problems with the screen heater. I teased it back out of the way.
So if you have a multimeter do the sequence of checks above to try to narrow down the cause. It could mean the difference between £1000 ish for a new screen or a few pence for a poor connection. Electrics can be a right pain to troubleshoot, especially on a Morgan with less than brilliant wiring diagrams.
There are cheap multimeters that can do a decent job on basic circuit testing so no need to go up market. Remember the days of making up a tester from a bulb and wires for testing for current? A battery in series to check continuity.

I had my heated screen replaced under warranty.

The elements just in front of the driver stopped working, although the rest of the screen was working just fine.

Oakmere dealt with it, no quibble, and seem to have fixed some leaks too at the same time.

So I guess they are a point of failure...I’ve had heated screens on a few cars and never had a problem with any of them, so seems odd that the Mog seems prone to this failure.

Most of the screen elements in my '56 Ford Fusion (pre-owned) were broken. Fortunately it also had the fan de-mist, but that takes longer to clear.

They did remove the dashboard and checked the element separately
The fault is definitely in the element and not the wiring
They are fairly familiar with Morgan cars

Mine failed due a connector separating behind the dash. Easy fix.