My arrangement had no electrical parts. The relays were the type that have spring backed contacts and so they do not instantly open when the coil switches off.
To do it with four relays the trick is to have the first one latch on with a press of the button, while the other three operate in sequence with the last one releasing the latched relay. So a very short press will latch on while a slightly longer one will release. It will probably require a button with two sets of contacts.

 

The one I showed is a single P.B. relay flip flop circuit, one push latch, second push to unlatch.

 

The one I showed is a single P.B. relay flip flop circuit, one push latch, second push to unlatch.

It certainly looks that way, Max. Not sure about the 100MFD capacitor/30 ohm resistor part, though. I am way to much into ladder logic, after years of relay circuits.
I guess that the TS did not directly specify the voltage. My circuit built in 1957 used Allen Bradley 120 volt relays with 10 amp contacts. As I look back at it now, those contacts were eve good for 480 volt loads. The insulation was long and the contact gap was at least 1/8 inch, and they were all double-make or double-break. Not available any more.

 

No response from the TS since the original posting but I think (IMHO) that my post in #16 will work using the relays the TS listed.
It's a true press and release action to set and reset not dependent on the hold time of the press.