A common trick (also often needed when using non-gel ballpoints) is to add some extra weight to the pen (for example, put a small glass jar/cup upside down over the pen, or use some large machine nuts).

Beware that this is harder on the servo lifting the pen, so you may want to order a few extra of those (also at TaoBao/AliExpress). I've switched from the cheap SG90 servos that are often used to the only slightly more expensive MG90S with all metal gears that seem to do better.