I'm having some odd fan cycling problem on my Carrier furnace. It has
behaved oddly ever since it was installed. At the furnace controller
card no yellow wire is attached. The voltage on the Green wire is
varying and when it gets down to 18VAC the blower fan kicks off. The
red wire is a solid 27VAC.

I'm still using an old round Honeywell thermostat and I'm guessing the
mercury switch in the thermostat has gone bad. Is that a good guess?
When I get a new thermostat should I add a yellow wire?

Also, is the wiring diagram below essentially accurate as a typical
example?

http://xtronics.com/reference/thermostat_wires.html

Thanks!