Update-ish... I thought I'd try to eliminate one theory as it's a cheap and easy fix. I bought a used wiper stalk from ebay for £20 and swapped it over in my car. I thought this might be the solution as the 'new' one has much more defined clicks when you turn the intermittent dial, but alas it hasn't solved the problem. The speed does change slightly (as before), but not really with any logic (eg one setting isn't really any slower/faster than the other). I only tested this out in the snow however, so perhaps I need heavier rain to test it properly - I'll report back if that actually makes a difference.
On a positive note, this almost certainly means the issue is with the relay and they're cheap to replace. The only problem is that the relay is difficult to access because it's high up behind the dash (I've replaced an indicator relay in this location before and it's a pain to get to). Although you can reach these relays, you can't 'see' them and there's no way of knowing which one you need to unplug. It was easier with the indicator relay as I could turn it on and feel it clicking (here's how to do that if you're interested: https://www.lexusownersclub.co.uk/forum/topic/126966-smarttap-flasher-relay-install-for-comfort-flash/ )
I've written a how-to on replacing the wiper stalk anyway (below) because there was nothing online about how to do this on a CT. All other Toyota/Lexus write-ups say you have to remove the steering wheel and airbag which you do not have to do on the CT.
How to remove / replace wiper stalk:
1) Turn steering wheel to the side to access two hidden screws. Remove these.
2) Separate the top and bottom halves of the plastic cowling. This is the trickiest part as you need to use quite a lot of force. They're held together with clips:
3) Remove the two white plugs underneath the stalk unit.
4) Using a small flat head screwdriver, push this clip down to enable you to slide the stalk unit away from the steering column.
5) Now you can install your new stalk and put everything back together in reverse order.
Please note: Replacing the indicator stalk would not be as straightforward - for this you would need to remove the steering wheel as it doesn't unplug in the same way as the wiper stalk.