This model from the 90s was named after the Swiss capital, Basel. This name was used before by PTT in the mid 80s for a different model. See also this link: PTT type Bazel (Tritel Elm)
PTT did not produce this phone themselves, but brought out an existing model under their own name.
It took me quite a while to find out what the original make and model was. Now I finally cracked it. At first I thought it would be Swiss, as PTT had a tendency to name their phones after cities of the country where the model originated. Not this time, though.
I opened it up to find more about it, but there was very little until I looked in the handset and found the name Siemens on the PCB.
It turns out this is a Siemens Miniset 310. The Miniset is a varied range of phone models Siemens made through the years, the 300 series having several versions with different buttons and functions.
I am happy I have solved this riddle.