Any details of what you are hoping to do with this wire would be greatly appreciated A wire from the positive terminal grounded under the seat would be a short circuit wouldn't it ?
If it doesn't take much current you should be OK. Fit an inline fuse to the live feed as close as possible to the live connection.
If you want the counter to operate with the ignition switch you would have to connect it to a circuit controlled by the ignition switch, or whatever arrangement the machine has.