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You have some luck, because you used Tamiya synthetic lacquer, which is one of the toughest hobby paint. In fact, your fist picture look like it's a standard process to do fine panel lines, if a cotton swap is going to be used to wipe the excess.
I don't know what type of ink the fine point pen is using, but if it's water soluble, water is all you need to clean the excess black. If not, use alcohol or enamel paint thinner.
Make sure you test on a scrap piece of plastic, or just paint the lid of the spray can with its color (, which I always do), wait until it's dry, and try those thinners to see if it affects the Tamiya paint. If not, it's safe to use, so just moisten a cotton swab, and gently rub along the panel lines, and you can achieve finer panel lines than just using a pen.
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