Gel ink is nearly impossible to remove from vinyl, but ballpoint ink should come off, especially if you’re able to get to it quickly. As with most stains, the longer an ink stain sits, the harder it will be to remove completely. Just to be safe, always test a new cleaning process on an inconspicuous area--say, the underside of a chair or seat cushion--to be sure you won’t be creating a “masterpiece” of your own.
Spray an all-purpose household cleaner, such as Simple Green, on the stain and rub gently with a soft cloth. Repeat two or three times if the stain shows any sign of lessening after the first application.
Rinse the stained area and wipe dry. If the stain is still present, dampen a clean white cloth with ammonia, apply the ammonia-soaked portion of the cloth to the stain and let it sit for up to five minutes.
Wipe gently at the stained area. Continue wiping if the stain shows any sign of lessening.
Rinse the stained area, clean and wipe dry. If the stain is still present, either apply a very small amount of acetone nail polish remover--by dampening a clean white rag, then dabbing it on to the stain--or spray an alcohol-based hairspray on the stain. The alcohol in either product makes an effective stain remover. Let sit for a minute or two, then wipe clean. Repeat as needed to remove the stain.
Never mix bleach- and ammonia-based cleaners, as the combination may release toxic gas.