So, I’ve dug myself a generously sized hole 😣.
I’ve been riding 3×9 forever (mostly because of the cost of upgrading), but a few weeks ago my front mech breathed its last and I decided to try a “cheap” conversion to 1x. This is what I have:

NW chairing
9 speed chain
10 speed Shimano M5120 SGS derailleur
9 speed 11-42 Microshift cassette
(Old) 9 speed shifter

And it doesn’t work. I can change from the highest gear (smallest cog) to the next no problem, but after that each change needs 2 clicks and I can’t get anywhere near the biggest cog. I’ve played around with the upper and lower limit screws and wound in the “B” screw as far as it will go.
I simply can’t afford to spend much more, and don’t understand the problem. I got the long cage 10 speed derailleur as googling indicated I would need that to cover the range of the cassette.
Would a goat link and my old (9 speed) derailleur work? Or a 10 speed shifter? (I know I would then have a “spare” shift but could presumably nullify that with the limit screws). I guess a 10 speed cassette and shifter would be the guaranteed solution but don’t want to go there unless there’s no other way.
Any help would be much appreciated!

9 speed Shimano and 10 speed Shimano have different pull ratios.

You need a 9 speed deraileur. As you have one, try using a goatlink. That’ll almost certainly work.

Thanks @boriselbrus. Worth a try

You might even get away without a link if you screw the b-tension right in on the old mech

Ive got wotking on two kids bikes using 2 quid roadlink copies you can get from ebay shifts perfectly.

Cool, thanks guys. Link ordered in case the B screw doesn’t sort it 😁