I own a 2001 VW Cabrio and after a dead battery.

The instrument cluster is a computer module and will not have a simple wire for the tach like older cars had. The information comes in on the "data buss". That's a wire or pair of wires that send digital signals between the many computers. When only one gauge doesn't work it is a problem with the cluster unless the gauge has a mechanical problem. Look at the pointer to see if it is below a small peg that sets the "0" position. If it is, it went there due to a current surge when you connected the new battery. The pointer is not spring-loaded. It is always looking for the shortest way to get to where it is supposed to be, in this case, "0", and that way is clockwise. The easiest way to solve this problem is to simply rev the engine to higher than half scale on the tach. As soon as the shortest way to get to where it is supposed to be is counter-clockwise, it will go there, then follow engine speed back down.