There is no such thing as "T4 to K-mount" adapter.
T4, by design, does not allow full-aperture metering, which is a feature of K-mount.
The later TX is very similar to T4, but with full-aperture metering. This additional feature prevents TX adapter from fitting onto T4 mount. TX to K-mount adapters do exist, but are somewhat rare.
If you find a TX to K-mount adapter, you can use it with T4 lenses but you'll need to do a simple modification on either the T4 mount, or on the adapter. It's been a while so I'll need to dig up my notes. But IIRC, the modification on the adapter involves removing some parts, and is reversible. I'll post back if I can find my notes and photos of the modifications.
T2 mount, on the other hand, is something totally different.
Edited to add:
I found my old post:
Modifying TX adapter to work with T4 lenses
Here is another thread on similar subject:
What's the value of having a TX mount over M42?