Monitor if TX+/- ethernet pins are sending data
No, for your case there is no simple and cheap way to light up a LED when there is a data packet sent.
During the time when the 100M link is up, there is a constant transmission of IDLE pattern being transmitted, and it is scrambled with pseudorandom sequence.
Basically the simplest and cheapest option is to design (or buy) a two-port Ethernet switch and use the activity LEDs (or MDIO interface) it provides for monitoring data transmission.