I would like to invoke a fallback function of a contract from Mist Wallet. However, I am not able to see it in the drop down list of functions.
Fallback function may be invoked when you send a transaction to the contract address The condition is that
data field must not match to the any signature of any contract function. In this case fallback function is invoked.
Leave data field empty and send payment to the contract is the usual way to invoke the fallback.