If you do not want to run the standard Python, you start the installer (or tl-setup) with PYTHON set to whichever Python you want. That one will then be used by every other portion of ThinLinc via the python-thinlinc symlink.
It is very easy to undo this work though, as re-running tl-setup and forgetting to set PYTHON results in tl-setup reverting to the standard Python. This gets worse with the new menu icon, where it is impossible to specify a special interpreter.
We should consider having tl-setup (and possibly install-server) respect any python-thinlinc currently set. That would also make the policy of "when in doubt, run tl-setup" more safe.
Note that this is mostly a Solaris problem as that's generally the only place where you tend to have multiple Python installations.
The ability to choose Python interpreter was removed on bug 7566 as we don't see a need for it on our current platforms. Hence this is no longer an issue.