The transmission in my Toyota MR2 Spyder was failing Video:C56 5Th Gear Popout.m4v. Rather than repair this worn out transmission, I bought a JDM transmission I was told was paired with a 1ZZ engine. This JDM supplier had several engines/transmissions and wasn't sure exactly which car it came from but said it should be from a Celica GT. I could tell it was definitely a front wheel drive transmission because of the shifter shaft, linkages, and cables.
In order to verify it was a Celica GT C56 transaxle, and that the gear ratios and final drive ratios were the same as my stock MR2 transmission, I needed to dig a little deeper.
Gathering information from Wikipedia and MidshipRunabout.org, Monkeywrench Racing, and other sites, I gathered the clues to figure it out.
The casting marks are not a reliable way to determine, as the C60 casting mark does not mean the transmission is a C60. Determine if it is a 5-speed or 6-speed: Look at the end cover.
Does it have a VSS hole cover? It looks like 00-05 celica/mr2 and 03-08 corolla/matrix/vibe have the cover. E110 Corolla transmissions might have the VSS cover, I'm not sure. The E110 did not come with a 1ZZ though. An MR2 Spyder transmission would have the shifter shaft mounted on the back, not the front. SMT transmissions from an SMT MR2 would have the LUK equipment. I believe the C52 has a different number of splines on the axles, so counting the splines on the differential might give a clue.
The new transmission has a VSS cover, it also has the shifter shaft facing the front, and it's definitely a FWD 5-speed. So it seems it would be either a 00-05 Celica GT or the 03-08 E120/130 Corolla/Matrix/Vibe transmission.
To make things easier, the C52 from a Celica GT has a 3rd gear ratio of 1.392:1 and a final drive of 4.312:1 1 revolution of the input shaft / 1.392 / 4.312 = .1666 turns of the output shaft. give it 3 spins and that's .4998 spins of the output shaft. 6 spins = .9996 revolutions
I made a C5X transmission spreadsheet to figure out the ratios, and the difference would be easily visible at 6 turns of the input shaft. I put it in 3rd gear, which I determined after I found reverse. I marked the input shaft with a sharpie, gave it 3 and then 6 spins, and the ratio is correct. This should be a 00-05 C56 Celica GT transmission.