The sign said the machine to issue the seat supplements was at the east entrance — the other side of the gates from me, of course.
The guard at the gates understood me, but said I must exit back the way I came, i.e. all the way back to the west entrance. That side of the station 'belonged' to the other railway company, and there wasn't a machine to sell the ticket I needed. I could either walk the really long way around by road (not through the station) or queue at the general ticket office.
So I missed that train.
In general, I found the train ticketing system for regional or long-distance trains needlessly complicated compared to Europe, with base tickets, express supplements and seat reservations all separate fees, and coming as 1, 2 or 3 bits of paper depending on I know not what.
On one occasion a journey with a transfer came on 7 separate tickets. (Of course, the Japanese approach to this problem is not to simplify the ticketing system, but to invent a machine that can suck in all 7 tickets, cancel the relevant ones, and discharge them neatly arranged.)
For example: You'd explain to the staff that you want to use the toilets, and they'll hand you a plastic NFC token coin, limited to enter and exit at the same station. You use that to enter the paid area, go to the toilet, then deposit the coin in a special slot to exit.
>Gate guards usually hand you a slip that explains the situation at the other gate or when leaving again.
That was done in the past, but it's quite nice that they just hand you a token now.
Alternatively, train stations in the Netherlands have done away with fees for entering and exiting the same station altogether. Toilets within stations often charge a €0,70 fee, though.