Your second picture link is not opening for me, however the first picture link for the front console appears to be a relay connector, not a flasher.
As Willie59 stated, standard flashers typically have 2-3 terminal pins. Additionally Case does have a special flasher unit that controls both turn signals and 4-way flashers that are used on the K and other series backhoes. It has 7 terminal pins on it, 2 of which are smaller in size.
Typically the unique Case flasher is located in the steering wheel column shroud. Based on your picture, I think you are dealing with the standard relay though.
To confirm what you have, how many wires are in the connector and are all of the terminals the same size?
Assuming it is configured for a relay, the relay used in the front console is standard. However just like fuses, relays have power ratings so you need to make sure you get the correct relay for the application. I believe I recall that these relays on the K are 30 amp, but don’t quote me on that.
They are used on many pieces of construction equipment (dozers, skid steers, etc.) so your Case dealer would probably have one in stock and you would be sure to get the correct power rating if you purchase through a Case dealer.
As installing a relay that is underrated for the application can cause a lot of damage including fire, I personally would play it safe and get one from the dealer and chalk the cost up to cheap insurance.