From what I gather, 7.1.2 and 7.1.3 were only shipped with specific systems. You couldn't get them through retail channels. I'm not sure if the install discs would even work on any other system that they weren't designed for.
To the best of my fading memory, System 7.1 Update 3 is not synonymous with a System 7.1.3, wot of there never was one. However, there was/is a Finder 7.1.3. Some reference to the matter can be found at http://68kmla.org/forums/viewtopic.php?f=7&t=8770&p=89204.
I have used such a retrofitted System 7.1 in a RAM-throttled Colour Classic (recte a Performa 250), as well as in a IIci (with umphed-up RAM), but the IIci Macs have now all passed-on to OS 7.6.1 in keeping with their DayStar 030 and 040 cards.