RS232 is simple: line is -5 to -12V when resting, and +5 to +12V when sending.
You can find description of /INVALID output in datasheet of MAX3221. It is simple:
The INVALID output notifies the user if an RS-232 signal is present at the receiver input. INVALID is high (valid data) if the receiver input voltage is greater than 2.7 V or less than -2.7 V, or has been between -0.3 V and 0.3 V for less than 30 ms. INVALID is low (invalid data) if the receiver input voltage is between -0.3 V and 0.3 V for more than 30 ms.
So, in simplest way, you need to find if signal is out of range between, let say, from -2V to +2V. You can do it with 2-wire dual colour light diode. It will be one colour if line is in "0" state, or other colour when line is in "1" state. And RS232 connection will be absent if the diode is black.
There is the circuit of RS232 Break-Out Box using such method, that allows to monitor the state of all lines:
Full article about that device is here: http://www.marcspages.co.uk/tech/3105.htm
May be it will be enough to monitor only one the "TX" line in your case.