Right, I haven't seen a full write-up about this, and I know there's a few people that want to do it.
This is a very easy modification and can be done in 5 minutes. The only con I can see from this, is when you put your key in the ignition; it doesn't light up any-more. It will when you turn the ignition on, though. Everything else still works as it should.
I wasn't and am still not sure if you have to take the side panel off where the fuel cut-off switch is and the one under the steering wheel, but mine was already off. I think you may struggle if you don't, as the panel under the steering wheel may get in the way.
If you do this mod without taking these panels off, let me know and I'll edit the post accordingly.
This beeping has annoyed me for years and to find out I could have it done in 5 minutes was both a relief and little annoying.
Here we go:
Take the side panel off, I got a flat-head screwdriver in to do this:
Now, you won't see the screw as I'd already had these bits off, but there will be one in there, remove it.
Now the panel under the steering wheel does come off quite nicely. I recommend a more forceful tug here, in order not to break any clips. Don't be gentle. Although, don't put your full strength into it.
Now, you're going to see 3 screws under the steering wheel plastic. Remove them
Give it a gentle pull from either side from the bottom and it should separate with the top half quite easily.
Now if you look at the ignition barrel, there should be two green cables. It's the cable that goes directly into the ignition you want to remove. There is a tab at the back which you need to hold and pull to get it out. It took me a few attempts to get it out though.
Now we're done.
Get the bottom of the steering wheel and top back together, line the panel that goes under the steering wheel, make sure all the clips line up the holes, and put the side panel back on and you're done.