Just sharing for anyone wanting to know how to get to immigration on the BTS. I took this route today, and it was really easy.
1. Take the Sukhumvit Line to N17 Wat Phra Sri Mahathat
2. Transfer to the Pink Line (MRT), P16 to P12 (Government Complex)
3. Take Exit 4. Go down the stairs, take a left, and walk (200 M) to the complex entrance, where you will see a blue guard shack.
4. Take Route 1 or 2 Electric shuttle to Building B
You can use a single-ride ticket if you don't use the Rabbit Card. A one-way from Phra Kanong BTS is 91 baht, so it could be more or less depending on where you are coming from.
The whole trip took me about 1hr 10 minutes. I've taken the BTS to Victory Monument, the bus, and a Grab from P16, and today's route was the most straightforward and cost-effective.