That sound you were having trouble identifying was from a satellite and it was on the downlink side; it was AFSK (Audio Frequency Shift Keying) and it uses Bell 202 modem tones at 512 baud for POCSAG paging (RPC-1) used by the "outdated" but still quite viable pocket pagers aka "beepers". This format is NRZFSK (Non Return-to Zero Frequency Shift Keying) which explains the perfect square wave you observed and IS 2 different frequencies +/- 5 KHz from center. You were 100% correct! Good show!
