Someone very helpfully reverse engineered the compiled .NET DLL for the Wireless@SG on Windows. The writeup is here, while the small Python script for connection is found here.

user:~$ git clone git@github.com:zerotypic/wasg-register.git
user:~$ cd wasg-register
user:~$ pip3 install -r requirements  # pycryptodome & requests
user:~$ python3 wasg-register.py 65{{phone number}} {{DOB in DDMMYYYY format}}
OTP will be sent to mobile phone number 65XXXXXXXX
Enter OTP to continue: XXXXXX
Credentials:
	ssid = Wireless@SGx
	eap = PEAP
	phase2-auth = MSCHAPv2
	identity = essa-XXXXXXXXXXXXXXXXXXXXXXXXXX@singtel-wsg
	password = XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

Then as per usual, the GUI example shown here: