Thanks for all the help in this thread. I decided to follow the advice of some of the earlier suggestions here and settled on this:

https://www.ebay.co.uk/itm/112603916459

I am aware that you get what you pay for, but as I have mentioned, I do not ride at night but do ride frequently in Scotland. That means riding in wet, dull conditions often. So, my main requirement is to be seen rather than to illuminate the road ahead. So, I am hoping that this will satisfy my needs without a sizeable outlay and they are certainly better than my current set of lights.

Thanks to all who contributed.

Looks like an intelligent choice. German standard lights are usually more expensive than other lights. This one tells you the battery capacity in both lights and they are reasonable. A lot of the more expensive lights seem to consider battery capacity a state secret. USB rechargeable batteries are good for between 300 and 500 recharges so when it finally dies tossing the light is not major tragedy. It has more bells and whistles than I would expect for the price.

I found it on Ebay from a China seller but with a much cheaper USB tail light for $18. That's OK since you can buy a 100 lumen light identical to the Blitzu 100 lumen tail light for less than $4.
The run times there are
(15LM/48H)-normal(200LM/8H)- very bright(400LM/4H)-flashing(400LM/16H).
Automatic light adjusting energy-saving mode+ bilateral warning lamp

If you ride enough to be picky, then be picky! Your emphasis on light distribution instead of light output is refreshing. There is a reason some car people (myself included) still insist on Cibie headlights instead of million-lumen Bloo Blinderz HID junk from the fleabay. Seeing is critical; blinding other people is dangerous, arrogant, and counterproductive.

I am not serious enough yet to spend up for a B&M, but I definitely do want an automotive-style low beam cutoff. I think I'm going to try the Ravemen PR900. The combination of both low and high beams, with different light distribution, makes more sense to me than adjustable brightness does.

In this case, you're going to stick to the marketing of this lamp.
It's not a real cutoff, so very far away from aotomotive-style cutoff-beam.
Take a look:
StVZO bike lights - what it is really about ? - Light-Test.info

If you need more information, just ask.

By the way, lamps with real cutoff-beam are available already below $40.
https://www.ebay.com/sch/Lights-Refl...9&LH_PrefLoc=2
https://www.ebay.com/itm/MEILAN-X1-B...sAAOSw4PxaCivG

It may not have a Cibie/projector grade cutoff, but from the photos I've seen, it's reasonably good - certainly far better (if aimed carefully) than a full round beam.

I thought that the Ravemen stuff could be toggled between low and high beam via the remote button, but apparently not. That's a little disappointing.

Thanks for the links. I'll take a look. I am still sorting out the options for a rechargeable light (I have no dynamo). Unfortunately there are so many counterfeit products and so much shameless junk available that it can be hard to know what you are actually getting.

Actually you must not own one, I own a couple of their lights. And in comparison to automotive they are actually very similar.

They arent the hard cut off of more expensive lights but there is nothing "marketing" about it. The cut off still allows for a small amount of spill to spread above. Just as automotive lights do.

Well...that depends a lot on where you live and what you drive. I probably shouldn't have introduced the comparison to automotive lighting.

Outside of North America, automotive low/dipped beam lights typically have a very crisp cutoff with little or no light above it. US lights were different (read: terrible) for decades because our regulations actually required a soft blob of light with no sharp cutoff. Cibie, Marchall, Hella, et all sold a lot of lights to the sports car crowd back in those days because they actually produced a useful spread of light, unlike the sealed beam glow worms our cars came with.

Some US market cars still have poorly designed headlights with spillage above the cutoff.

At any rate, the Ravemen stuff is probably good enough to be effective, and at a reasonable price.

What do you tell someone when the budget is unreasonable? Think out of the box.

One thing is to get a subsidy in the broadest sense of the word.