Checkering is done with small 90 degree toothed checkering cutters that look a bit like a 1/2" long piece of a file on a handle. There are spacers as well as multi-line cutters, designed to make the job look even and keep the lines parallel. Not trying to sound negative, but a rifle like your Belgian Mauser is no place to start learning. If you want the checkering recut, give it to an experienced stockmaker to do. PM me if you want a quote, I am a stockmaker.
Never try to educate someone who resists knowledge at all costs.
But what do I know?