Yes, I've installed the 64 bit Oracle client first into directory C:\oracle.
Afterwards I've tried to install the 32 bit Oracle client into directory C:\oracle_32bit.
As stated before: the GUI of the installer suddenly disappeares and no error messages are logged.
Pl post the last 100 lines from the install log - the name and location are documented in the Install Guide in the Troubleshooting section
I've followed Doc-ID 1530206.1 - which solved my issue.
Thanks for your support and help anyway.