VAIO laptop's wireless indicator blinking when connected to access point

You are right, it is a driver issue or rather it's a feature!

According to the documentation (which seems rather hard to find atm) (sudo modinfo -p iwlegacy the driver iwl_legacy has an option led_mode which controls exactly this behaviour (namely blinking on sending/receiving packets).

You can turn it off by creating a file called wifi.conf in /etc/modprobe.d (obviously as root) with the following content:

# Disable blinking
options iwlegacy led_mode=1

Then restart for the change to take effect.
You could also just rmmod and modprobe the iwlegacy and iwl3945 drivers, but that's a tad more complicated.