First I would refer you to this if you have not read it:
http://docs.info.apple.com/article.html?artnum=1605
Pina's Macintosh Repair & Upgrade book is invaluable to the old Mac user. However, it is often unclear and contradictory to published Apple info (not unusual since Apple often contradicted itself). In particular I would ask you to re-read Pina's statement about the speed signal in the last paragraph of page 193. Like many statements he makes in the book you really have to read it several times to understand why he's saying it. However, he gives this info so you won't mix up your internal drives and cables. I'm afraid you mis-interpreted this to mean you had to physically cut wires on your drive, which already had taken Pina's observation into account. Besides, Pina's advice is for internal drives and as you know the external pin-outs are completely different.
That said, it might be worth a look at the Apple IIGS 800K floppy controller pin-outs to see if there is a signal line that might be cut which would prevent the LED flashing and disk access.
Now, as to your problem ... thank you for clarifying. You mention in your initial post that the internal drive "pulses". So I wasn't sure which problem you were trying to fix. Frankly the flashing LED is the least of your problems since that goes away after the system is in use and the pulsing does not (at least with an 800K internal drive, the 400K works fine) ... so much for a quiet system. This is on of those things that I shake my head at because I know what you are saying. It bothers me too, like dust under the refrigerator. Frankly (and I mean no offense here), but the time the Mac is on without a system disk working is so brief as to be a negligible issue ... particularly when you consider the following:
What you and I are both doing is a HACK. PERIOD. The 800K drives may well work with the 128K (and indeed Apple intended this from the beginning when the double sided drives became available, but their strategy changed when they created HFS), BUT once Apple changed to HFS, they made no attempt to make them compatible with the 64K ROMs without the HD20 INIT and HFS support. For whatever reason the A9M0106 and MFD-51W-03 drive doesn't care, possibly to enable compatibility with the Apple II. Notice Apple says specifically NOT to put the older drives in the A9M0106 external enclosure. Therefore, AS A HACK, you are using something that is not designed to be compatible with your system and therefore is likely to do lots of things that bothers you. I personally have banged my head against a wall simply because I wanted something to work in a manner in which it was never designed to work, simply because it bothered me. That said, certainly Apple must have known the A9M0106 worked without the HD20 with 64K ROMs (as well as the MFD-51W-03 drive). Since very little is known about the exact release dates and discontinuation of the external drives or the rational behind Apple's design, it has been assumed Apple intended the A9M0106 as a universal replacement for all of their previous 400K & 800K drives and as such, an original 128K/512K Mac which still needed a 400K drive could buy it as a replacement external with an eye toward upgrading in the future. If so, they must have also known the LED would flash and drive accessed until a system disk was inserted with or without the HD20 INIT. And just so you know ... when the A9M0106 is used with a Mac Plus, the LED flashes once upon startup as it is being accessed by the Plus looking for a startup disk – the difference obviously being that the 128K ROM knows how to handle the drive response and patiently waits. With that in mind, I doubt cutting any cable will stop the problem without rendering the disk useless. All in all the continual disk access at startup is a small trade off for use with the 64K ROM.
I do hope you find a solution, however unlikely and I must admit your post has peaked my curiosity about testing various combos of my external drives with my 128K to get to the bottom of not only the flashing LED but also the pulsing, which Pina himself fails to explain (I mean really, if the speed control is already isolated from the drives, then why do they pulse?).
Finally, I am thrilled you are helping to clarify the mis-information on the web. I am certainly not looking to take credit as discovering this, or certainly overshadow your accomplishments ... if anybody deserves the credit it's Larry Pina! My goal is to clarify the mis-information and to make working with an old Mac in an Intel world easier for the Mac enthusiast. Particularly when it comes to pre-system 6 and MFS systems. I will not state anything that I myself have not tested. That said, I must tell you that while this 800K drive works without the HD20 INIT, the actual 800K External Drive M0131, sold for the 512K & Mac Plus will NOT work. Also, on a 64K ROM system, you CANNOT use HFS formatted anything without the HD20 INIT which will not load on a 128K. On a 512K, even with your drive, you must have the HD20 Init in order to write HFS formatted disks with a System 2.1 or later. System 2.0 and earlier will write MFS ONLY with or without the INIT. So, be very careful about saying a thing is right or wrong unless you've tested it personally. Also, your posts seem to indicate that you are limited to 400K without the HD20 Init. on your drive and that's how mis-information gets around.
In any event I look forward to your future discoveries ... happy hacking!