From the tabook, the 701C/CS was specified to use 92G7259 (4MB), 92G7261 (8MB), 82G7293 (16MB) or 92G7281 (32MB) 3.3V SODIMMs. Searching for those FRUs in the same tabook, shows that none of the other systems of that day referenced those part numbers.
Regarding the first ("cheapest 701") auction and the photos that are included... showing that the module passes the BIOS memory test in some cases is not enough. I'd rather see the results from several passes of memtest86+, but I digress.
However, there is some important information to be gleamed from that photo. The module has 4 Samsung KM48C2100A devices on it. Looking up that datasheet shows that the part is a 2M x 8 FPM (Fast Page Mode), having a 2K refresh. That there are 4 of them means that pictured module is an 8MB, not 16MB (the photo of the back side shows it is not populated). My
guess is that the seller saw "16MB" in the BIOS and assumed that's what the module is, not realizing that there's 8MB soldered onto the motherboard. Or I could be wrong and he does have an actual 16MB module and just used an 8MB module for the picture.
edit: Just noticed that the KM48C device is 5V, not 3.3V. I would think that module may not work correctly in the 701C.
The first three eBay auctions reference EDO (Extended Data Out) modules. In
some cases, you can substitute an EDO module for an FPM, but usually not the other way around. The difference has to do with how the data out pins are controlled during "page reads". The short version is that FPM devices turn the output pins on and off from one address to the next, while the EDO devices do not.
Can the 701C tolerate EDO modules? From looking at several posts here in the forum it seems to be. The most important thing to note is that the module should use 2K refresh devices. This is basically identical to the difference between PC100 "low" and "high" density modules. So, to answer your question:
http://www.ebay.com/itm/200758250154 Micron MT8LDT432HG-6 should work,
if that's what the seller is selling. That part number in the photo is for a 4M x 32 (16MB) FPM module using 2K refresh. Note that the auction title says "EDO" and "MT8LDT432HG-6X" (the "X" at the end stands for EDO). I would contact the seller before buying.
edit2: This one
http://www.ebay.com/itm/321360365980 should also work. The Micron device is the same MT8LDT432HG-6; the 32MB module is EDO but uses 2K refresh. It
might work, although both are said to be untested.
edit3 9/26/2014: Well, it looks like I was wrong in saying that the 32MB (Hitachi HB56RW832DZJ-6LS/C) is EDO. I just found a datasheet for it and it's a FPM. Since this is apparently what the 701C was designed for, so much the better. I can't remember what led me to believe it was EDO at the time...
ref:
http://www.datasheetarchive.com/dl/Data ... 164637.pdf