This indicates a possible issue with either the tip of the Ethernet cable or the LAN port on your modem where the cable is connected.
To resolve this:
1. Replace the Ethernet cable with a new or tested one.
2. Try plugging it into a different LAN port on your modem.
3. After doing so, check the status of the indicator lights again.
If both lights start blinking or stabilize as expected, the issue is resolved.