Special RAM for Performa 6360?

Your Performa 6360 uses an older type of memory: 5-volt, 168-pin DRAM DIMM, Fast-Paged Mode, 70 ns or faster, with a 2K refresh rate maximum of 64 MBs. The motherboard has 8 MBs of soldered DRAM. The 3.3-volt PC-133 DIMMs that you tried are what is classified as SDRAM. All SDRAM (PC-66, PC-100, and PC-133) is incompatible with the 6360.

It may be compatible — I can't determine by the photo. You need to know the refresh rate of the chips on the DIMM. For complete compatibility in a 6360, it should be 2K. A DIMM with chips having a 4K refresh rate (which is common) will function, but a 6360 will only recognize it at ½ of its stated density. If that's a 64 MB DIMM with a 4K refresh rate, it will be recognized as a 32 MB DIMM in your Performa. If your goal is to have 64 MBs of recognized memory in each slot, each DIMM must be rated as 2K refresh.

I enlarged the photo on that ebay listing to examine the chips contained on the card. They were manufactured by Hynix Semiconductor: HY57V651620, with specs that indicate 4 Banks x 1M x 16-bit Synchronous DRAM (SDRAM). The TC-10 timing (which isn't the same as refresh rate) would be consistent with 3.3-volt SDRAM, PC-66 or low-end PC-100. This memory can't be used in a Performa 6360. You need the older and harder-to-find 5-volt DRAM with a 2K refresh rate.

I spent some time this morning searching and struck out on Crucial and Other World computing. However, Data Memory systems:

http://www.datamemorysystems.com/apple-powermac-pre-g3-memory-upgrades/

says to e-mail or phone for availability of older systems' memory. I've bought from them before--I trust them.