"True 120hz" is still very rare, yes. If the TV would accept true 120hz (and not some pseudo-interpolation)...you should know it for sure.
Are there any hacks that will allow one with a regular television to use shutter glasses?
I was thinking of using an HDMI splitter, connect one end to the TV and the other to an IR dongle sitting atop the television.
Is there hardware readily available for this? Or are there sites that explain exactly what infrared signal is sent to the glasses?
Or maybe I could use it without infrared and just calibrate it once. How bad could it desync?
You focus on the IR signal - but the IR signal is not the essential part for 3D capability. The IR simply transmits the 3D sync signal to the glasses. Whether this happens wireless (via IR) or wired...is not really relevant.
It is more important whether your display is a LCD, CRT, Plasma etc. and can (in theory) display 3D in some way.
If its a Plasma or CRT...you *COULD* do some hacks eg. feed it an interlaced signal, aka L-R-L-R. Even if the TV would only support 60hz there could be some way to get some 30hz Ghetto 3D - but as said it would need to be a CRT or Plasma since LCDs do not support interlace.
Then you would still need to sync your glasses with the signal - there are some solutions eg. which take the signal from the VGA port. Like the edimensional shutter glasses where there is a "dongle" which you connect to the VGA port - then to the CRT...and the "dongle" electronic itself generates the sync signal which is then transmitted to the glasses via the IR diode, either using wire or IR wireless.
Or are there sites that explain exactly what infrared signal is sent to the glasses?
http://www.stereo3d.com/vesa3.htm
This is basically very simple...its a single TTL signal "stereo sync". Some 3D TVs have that VESA connector (circuit inside TV generates the signal), or its at the Dongle and the electronic in the Dongle generates the signal.