That said, I can't resist to offer my opinion on pen-lines in general. In brief, and being very frank: They are an old fashioned way of hiding poor composition or a lack of printing ability. This is not always the case, but it is often the case.
The condition you described is typical, but I would argue: Make sure the white disturbance at the border of the print is not part of your composition, or, print it out, spot it out, and if all fails, let this one go.
In my opinion, the composition and the printing need to hold the image together, not a crutch called pen-line. If I start thinking about a pen-line, chances are, there is something wrong with the image or the printing. Some go to the extreme and use a pen-line with EVERY print. That's a clear sign of a misunderstood technique in my eyes.
There are exceptions:
High-key images often benefit from a pen-line. They contain a lot of white, and mounted on white mount-board, the image might not hold together otherwise. Yes, pen-lines work with some high-key images.
An off-white, even light gray, mounting board can create an automatic framing similar to a pen-line. That's OK in my view, because it is not as obvious and attention-grabbing as a pen-line.
A black frame itself is a pen-line in a way. Yes, but it serves the function of isolation the print from the wall, not to hide a poor composition.
OK, these are just my opinions and not intended as a demand on others. But, do yourself the favor and as soon as an image screams for a pen-line, ask yourself why that really is. Put a pen-line around it if it helps, but don't use it as a general crutch. A good image does not need a pen-line to hold together. That's done by the composition and supported by the printing.
Again, just my opinion.