Emulator

Just chiming in that I have had this issue reported to me a few times from linux users who purchased my adapter. I don't use linux myself however so I cannot confirm.

I am also experiencing this with genuine WML-C43 adapters (including one out of my wii).
Tested with Batocera Linux 36 and Ubuntu 22.04. Other adapters will pair and remember pairing but the real deal wii one will not. The controller will briefly flash a couple times as if the connection is being rejected or perhaps the link key isn't being properly exchanged?

Not sure how to get diagnostic logs for a passthrough adapter but happy to help if someone tells me how.
Windows with the exact same adapter is totally fine.

This can be fixed by blacklisting the Nintendo bluetooth USB module in the btusb.ko file. I used binary patching to replace a previously blacklisted device with the nintendo one.

Make a copy of the /lib/modules//kernel/drivers/bluetooth/btusb.ko file for editing.

Use a Hex Editor > Find string "5C 0A 33 20" and replace with "7E 05 05 03". Then at the very bottom of the file remove "~Module signature appended~".
Backup your existing btusb.ko file. Replace the btusb.ko file on the target device with the binary patched version and reboot.

This replaces the item "Broadcomm BCM2033 without firmware" device with the nintendo bluetooth module and should be safe to do unless you happen to have a BCM2033 without firmware installed in your system...

Bluetooth passthrough for the wii module now works as expected.

Also having this issue on my Steam Deck (Running SteamOS 3.5.7) with a J27H002. Dolphin version 5.0-20950
Works fine for the first sync as described but as soon as you restart the game it doesn't sync and has the same blinking issue.
Have tried to edit the btusb.ko file but did not have success (for me it was stored in a btusb.ko.zst (path: /lib/modules/6.1.52-valve12-1-neptune-61/kernel/drivers/bluetooth/btusb.ko.zst) file, which I had to extract, edit, then re-compress). Guessing the btusb file is different on SteamOS and I don't have enough experience with hex editors unfortunately :(.
I have another BT adapter (some TP-link one) that can remember pairings.
Also not sure how to get logs out, I had a look in dolphins logs (View>Show Log) and there were no errors (idk if there are other places I need to check)

I also tried running through the process of hex editing the btusb module on my Steam Deck to blacklist the Wii BT Module, but all I succeeded in doing was breaking Bluetooth on my device until I put the original .zst package back in place. I wonder if there was something funky about the way those archives are compressed.

It would be great if we had a solution that doesn't involve editing system files (which for an immutable OS like SteamOS is more work).

AbbieDoobie wrote in #note-1:

Just chiming in that I have had this issue reported to me a few times from linux users who purchased my adapter. I don't use linux myself however so I cannot confirm.

Can confirm that your adapter works great under Windows, only Linux with issues which is no fault of your adapter.