why does my temperature gauge peg way past hot?

I have a rare '86 non turbocharged Pontiac Sunbird GT. After the
engine warms up, the "check gauges" light lights up, and the
temperature gauge pegs way past hot even though the car is not
overheating.  I replaced the temperature sending unit, drove the car
about a dozen miles with a combination of surface streets and
freeway driving.  At about 160 degrees the fault occurred again.  The
next step is to replace the more expensive temperature switch. This
is not the fan switch.  In 1986 Pontiac saw fit to make all Sunbirds
turbocharged, as standard. This 1.8 (112 cu in) engine is in a non
turbocharged  77K mile survivor car. Pontiac produced 118,118
Sunbird two door coupes, including the LE and SE models. Of that
number, I don't know many were GT's and how many were ordered
without a turbocharger. A search across the US and Canada
produced zero '86 Pontiac Sunbirds for sale, anywhere.  So the pool
of people with same car is nil, much less the non turbocharged 1.8
engine.
I sort of chimed in here because I saw that someone was having the
same problem,  albeit with a much newer Pontiac. I have yet to see a
solution here. Has anyone an idea or two?