What is a ’Pull Up Resistor’?

Did he reccomend a value for the resistor?  He is wanting you to apply power to one side of a resistor, and connect the other end of the resistor to the wire he specified. 

A pull up resistor is merely a resistor - I'd suggest a 10kOhm 1/2W carbon film or similar (not wirewound - if they still exist!). It should be connected between the tacho's signal wire and its +12V supply. It sounds like your ECU has an open collector output for the tacho, and your tacho does not have an internal pull up resistor (why should they - they attach to ignition coils!). The pull-up resistor pulls the open (collector) output up to +12V. When the output transistor turns on, its collector terminal is connected to ground (close to 0V - maybe 0.2-1V?). Hence the output is a square wave from near-ground to near +12V. They should have provided a suggested value, but 10k should be safe. I'd ask the before trying 1k. Either value is low power but 1/2Watt is a common size that is reasonably robust. But 1/4W is still ample.    The FYI ramble follows: "Open Collector" outputs are typically used in logic circuits - eg, CPUs, electronic controls/switches etc. It simply means that the output is either earthed/grounded else is floating. IE - a transistor is turned on to connect the output to 0V (zero volts) or it is turned off (high impedance) so the output "floats". Why do this? Because you can then interconnect systems of different voltages - ie, 12V, 24V, 5V, 3.3V etc. (Not their power supplies - just their inputs & outputs. Ignition points are an equivalent example - the points are either closed and shorted to chassis/ground, else open and floating. (It's the same as most ignitors, HEIs etc; though not CDI.) The points are pulled up by the ignition coil. For open collector outputs, there is nothing to pull the output up from ground. Hence the pull-up resistor. Most logic pull-up resistors are 10k Ohm (10,000 Ohms), but they can be much higher to reduce power consumption. They can be as low as 1k Ohm, but that can be too low for many circuits, and 100 Ohm is very likely to burn out logic & CPU open collector outputs. (Ignition coil ignitor open collector outputs are a special case that can handle say 12A switching - that's 1 Ohm at 12 Volts.)

I'm pretty sure they recommended a 1k resistor.  I've got it written down somewhere.