The cable between your Amiga and Modem MUST connect CTS,RTS, DTR, DCD, TXD, RXD and GND conductors. CTS and RTS are used for flow control handshaking. DTR is used to keep the modem on line - hangup occurs if it is dropped. DCD is used for carrier detection.
TXD 2 Transmit Data
RXD 3 Receive Data
RTS 4 Request to Send
CTS 5 Clear to Send
GND 7 Signal Ground
DCD 8 Data Carrier Detect
DTR 20 Data Terminal Ready