I just went into the darkroom and pulled out a recent test print. I knew that they gradations were 1/8 f/stops so I marked on the front of them, then I turned the print over and marked the rear of the print. I did this while the print was underwater, with the water at temperature of 24ºC, which is currently our tap water temperature.
I then took the print out and wiped it vigorously front and rear with with a squeegee, to emulate a worst case scenario. You will note that the colour of the ink is black under the water, but when dried (almost dry) on the seat on the verandah, the ink has changed to blue.
I rubbed and rubbed the squeegee over the front and rear of the print, where there was a blob of ink, it certainly streaked. However I know from decades of experience, if you let things dry, or put the paper though a paper dryer, which I have, then streaking is minimal to not being there.
This was done with a medium ball, black ink pen. Part number SPR4, which is manufactured in the USA.