I happened to test Corepure64 after reading that vesa doesn't support 64 bit, and realized that there were many TinyX servers, not just Xvesa! I know I know, old news to you, but this was a revelation to me, since inxi was failing to show any graphics data at all.
This is now running well in pinxi (next inxi, 3.3.32, which should be out within a few weeks), though there's no API type data I could find for Xfbdev, but that's fine.
The easiest way to install pinxi in TC is to first install the inxi tce package, which will install the dependencies, then to install ca-certificates, if you don't have it, then: wget -O pinxi smxi.org/pinxi which will grab the current pinxi, which you can then run fine. That's how I test and develop.
Graphics:
Device-1: VMware SVGA II Adapter driver: N/A bus-ID: 00:02.0
chip-ID: 15ad:0405 class-ID: 0300
Display: server: TinyX Xfbdev v: 1.3 driver: fbdev display-ID: :0.0
resolution: 1024x768
API: N/A Message: No display API data available.
Note that Xfbdev exposes in /sys the virtual_size of the display, which lets me, at least in my test system, get the screen resolution for a TC, but I suspect only this one. That data was not available with Xvesa, at least not in my tests.
Rather than add cludges, I just added in all the listed TinyX X servers, though I believe in the real world, the only ones likely to be seen or used are Xvesa and Xfbdev. Though I could be wrong, I had never heard of any other TinyX server before a few days back, so I am hardly a good source for this type of information.
This is by the way why packaging inxi for TinyCore is a useful thing, aside from just the inherent cool idea of such a tiny Linux in the first place, it exposes corner cases I would not have considered, that will often benefit all light distros of this type, not just TinyCore.