Hi all - I had been following updates on this thread for a while now, and wanted to post an update that might help provide some clarity on the timeline. In my case, I applied for Global Entry October 2018.

• For context, I've been living in the US since 2008, so the last "record" of my stay in India would have been my high school.
• December 2018, I had to go to India to switch visas, and I scheduled my PSK appointment (in Chennai) for the day after that. For the PSK appointment, I took my passport and all old passports (the one saving grace was that the address I currently use in India, i.e. my parents' home address, was the same as the one in my passport) - so no further "documents" were required.
• They initiated the police clearance certificate (PCC) and we got a call pretty much the same evening saying that someone from the local police station would come to my house to do an address verification. The constable came the next morning, and asked for one additional proof of identification - thankfully, I had my Aadhaar card, and that would suffice. I signed a copy of that for verification, and off he went.
• The PSK website got updated to read that background verification had been initiated.
• I submitted a "grievance" ticket in March, and got a response within two days that said my application was "pending with MHA and MOF"
• Yesterday, I got an email from GEP saying that I should consider enrolling through an on-arrival process and they'd added new airports - I'd never gotten these emails before, so out of hope I checked the GOES website and found that my application had been conditionally approved on May 23. Scheduled the first available interview in my area, and hope to have Global Entry, and more importantly, TSA Pre, shortly. No updates to PSK website still.

So, overall, if you count the date from which the PSK process started, my application took 5.5 months to complete processing. Though this is, by no means, short, I'm just glad that the process is complete. So, two big lessons I'd say are:

1. It really doesn't matter if you live in India or abroad; you need to have proof of address and will likely need to plan to be in India for at least a week after the appointment to make sure that you can be "present" for police verification. If the address on your passport is not the current address, be prepared to show proof of address with some other government-issued ID (Aadhaar, PAN card, etc.)
2. The process seems to generally take around 5-6 months if all goes well; the grievance ticket system seems to work sporadically, and the responses are helpful to a certain degree to know if PCC has passed and if the file has gone to the ministry. After that, they just ask you to call to check.
3. Stay patient and it will happen!

Hope this is helpful.