So in order to absorb the DNA sequence and store it away for his next incarnation, it had to be someone living in the United Kingdom at that time, someone who resembled the future "Fourth Doctor".
So far as I know, there was no adventure on screen in which the Doctor rode in a railway car, but if there was, it could have looked like this:
But if all else fails in finding a photo of Jon Pertwee at a train station or on board a train (even if it's from a movie!), then once again I'll just have to invoke the Khan-Chekov Encounter. There had to be some point in his exile where he rode the rails!
Why is it so important? Because I think that's how he came into contact with the donor of a new DNA sample......
Out of all of Tom Baker's Earth-bound characters from the 1970s who could possibly have met the Third Doctor, I think this train porter, who was on screen for less than a minute, is the best possible choice. The main reason I've listed above - if the Third Doctor had to take the trains, he may have eventually come into contact with the porter.
Plus with only forty three seconds of screen time, the porter doesn't come with much baggage i.e., backstory.
Why would the Doctor's biological imperative have chosen the train porter for his DNA sample? Maybe there is something to the idea that one's personality quirks could be tied in to the genetics. The porter had an off-beat sense of humor just as the Fourth Doctor would have.
But as was the case with choosing the template for the Second Doctor, there would always be the need to find the strength to face the dangers of the universe. And the porter would have great muscle strenght - as well as dexterity - from all the baggage he had to handle at his station.