I have a couple of old Alpha LED readerboard signs. I think the interface is really RS485. Maybe. I have a couple of manuals around here somewhere, one is an Operation manual, the other describes all the signals it requires. I'll see if I can locate them.
Assuming your using the RJ12 to D-SUB9 connector cable your currently using to connect to the PC then you will need to use either some form of Software Serial or a separate serial port (Mega) if your Arduino is connected to the PC at the same time. Your RS232 converter has 4 pins that need connecting to the arduinos 5V, GND and the relevant RX/TX pins. The protocol looks to be 9600,E,7,1 so this may rule out the use of standard SoftwareSerial library. Both links you supply seem to give comprehensive info on the protocol.
The eBay listing states
Notice:The chip max3232 is made in China,some customer find it not compatible after purchase.
So please make sure the chip is compatible with your own system before purchase.Thanks for your cooperation!