Twelvoltz is right that at least one bypass manufacturer has had some tach issues with GM trucks.
I've had a run of a few Trailblazers this season already, and on all of them, there's a wire harness that runs horizontally along the bottom of the dash---I get parking lights, brake, and tach all there.
I did just think of one other thing that could be an issue on the 2006+ Trailblazer.
1: When you activate the remote starter, and then the ignition turns on (you'll see the dash warning lights all come on together), does the starter motor crank immediately, or is there a small delay?
2: Leave the windshield wipers in the on position, and activate the remote starter. Do the wipers stay on during remote start?
The reason I ask all that is because the Trailblazer has the following under the dash coming from the ignition switch:
---Two constant power wires
---Two ignition wires; they show power in the Run and Start positions
---One accessory wire (orange) that shows power in the Run position only
---Another accessory wire (brown) that shows power in the Accessory and Run positions
---A starter (yellow) wire that shows power in the Start position
On nearly every GM car on the market, the brown wire can be left unpowered during remote start. I actually prefer it this way, as the brown wire powers up the wipers and sometimes the radio. By leaving it unpowered, the wipers are disabled during remote start, and on some models, the radio stays quiet too---no need to wake up the neighbors every morning with the radio.
However, on the 2006+ Trailblazer, if the brown wire is left unpowered, the starter motor will crank immediately as soon as the ignition circuits (pink and white) come on.
This will work well enough if the engine was just running....I'm guessing because it's still warm, still has residual pressure in the fuel lines, et cetera.
So basically, if the installer doesn't power the brown wire, the remote starter will start the car super fast, but it'll still work, and the installer will shrug his shoulders and call it done.
Inevitably, after the customer has the car at home for a few days or so and it gets cold enough, it often won't work reliably. Sometimes it'll still start on the second try, but not always.
So basically, see if the wipers come on during remote start, and if they don't, have the shop power up the brown wire during remote start.
P.S. I wouldn't replace your ignition switch. A properly installed remote starter essentially IS a remote-controlled ignition switch.
Therefore, even if the ignition switch were bad, the remote starter would still power up all the circuits during its runtime....the car would run perfectly, at least until you do key takeover and press the brake.
I've seen these ignition switches go bad where one or more of the circuits isn't powered up until the switch is replaced.
I think you can pretty much do your own ignition switch test, without taking the car apart.
White ignition 2 wire: Rotate the key just a hair forward from Off; this should make the battery light come on, I'm pretty sure.
Brown Accessory wire: This powers the wipers; do they work?
Orange Accessory wire: This powers the climate controls, you did say they worked.
Pink Ignition 1 wire: Powers fuel/ignition stuff; car wouldn't run without this
Yellow starter wire: If you're a tech I'm sure you know, but the engine would never start without this