Just to be more clear than clear: the oil presure device on the 3.8 carries both a proportional pressure sender (for the gauge) and an on/off switch for the fuel pump backup circuit.
with 4 wires
(The 3.1 oil pressure device has 2 switches..one that gives a meaningless "reading" to the gauge, and the fuel pump backup).
with 3 wires
www.avigex.ca/xport/instrumentpanel1.jpg
www.avigex.ca/xport/fuelinjection.jpg
NOtice also that you can test the fuel pump only with engine OFF by feeding 12V to that red wire (fuel pump prime connector on the diagram) that goes nowhere usually between the EGR valve and the MAF sensor...
BUt...but...I'm just noticing something weird in your original title: '96 TS did not have the 3.8...nor the 3.1: it was built with the 3.4 only........ahhh..yeah....but in Netherland....model year might be different....possibly a '95 labelled as a 96..for the time to go across the pond....
and some european models always kept the sharp front end...93 style..
...but with the Silhouette trim...lacking the traditional Pontiac twin grille...at least in France, this one a '95 with a 2.4 4cyl using propane
while other countries, like Sweden and Netherland, had this style, this one from Tom van Hooft in Vlijmen
,NL
.am I right..which is yours ? .post a picture if you can...