Relevant to the topic but from a different region in the country:
Recently, my friend and I were in Sikkim in my own WB registered vehicle. Due to a landslide on the road to Lachung, we decided to return to Gangtok, and planned a trip to Nathu-La the next day. Little did we know what awaited us in terms of getting the permit. The hotel-owner warned us that there was no way we could get the permit to drive to Nathu-La in our own vehicle. We said, we will see the next day.
After taking some advice over the phone from adc, we lined up at the permit office very early the next morning at 6 am, and true to what the hotel owner mentioned, our request for a permit was not entertained. Some of the fellows just laughed at us when we said that we wanted to go in our own vehicle. Hell, we were not even given a blank permit form. All permit forms are with taxi operators and none of them agreed to give us a blank form on hearing that we wanted to take our own vehicle. In the next few hours, we came to know that:
(a) Nathu-La permits are issued a day in advance. If you apply today, you get permit for the next day.
(b) Due to the bad roads and inclement weather conditions at Nathu-La, the Army may or may not give the go-ahead to release vehicles on the Nathu-La route for that day. If the Army does not give permission that morning, all permits for that day are wasted.
( c) Only 70 vehicles get permits per day.
(d) The Sikkim government ensures that all the 70 permits go ONLY to the local taxi operators (yellow plates).
(e) The only exception (i.e. taking your own vehicle or any vehicle other than local taxis) would be special permits from either the Army or the Government, which is over and above the 70 count.
My friend and I activated 3 Army contacts (friends of friends etc.). Two of them came back with nada. The third was still on but didn't look too hopeful at that time.
Meanwhile on advice from some of the local taxi operators (who by that time took some pity on us but not enough to give us a blank form), we visited the Tourism ministry at the Gangtok secretariat to try our luck with a govt. permit, but when we went there, we were told that govt. permits were issued only to motorbikes (unless of course you knew a minister or high govt. official).
Very frustrated, we returned back to the permit office around 11 am. The crowd of taxi operators had cleared by then, all 70 permits given out. When I again entered the office of the permit officer, he asked me to sit down. I asked him why I should not be able to take my own vehicle to any part of my country. Having seen off the morning permit rush, he then patiently explained to me about how the Sikkim government encouraged the issuing permits to only the local taxi operators in order to generate employment and income among the locals. Since the number of permits/day were very limited and the number of taxi operators hugely exceeded that number, during the rush tourist season, each taxi operator actually got a permit in a round-robin fashion, which was about 1 permit every 2-3 days.
Surprisingly after a few more requests and some back and forth arguments, the permit officer finally agreed to give us a permit to take our own vehicle upto a point which was just 4 kms before Nathu-La. He then said that we would have to park our vehicle there, and take a taxi cab for the last 4 kms. He even called a taxi operator into his office and made arrangements for us with that guy to take us the last 4 kms.
This was a mini-victory for us after over 5 hours of frustration, and the best that one could achieve under the circumstances. We thanked the gentleman profusely and after making the necessary arrangements and paperwork with the taxi fellow, we returned to the hotel.
The rest of the story is not relevant to the topic on hand, but in case you ask 'what next', here it goes.
Sitting in our room, drinking some local brew (note: brew could be tea), suddenly I get a SMS on my phone. The SMS is from a certain Lt.Col A.U posted somewhere in J&K (friend's friend - not disclosing name for sake of privacy) to immediately go and meet a certain Major V. of xx Division in Gangtok. His boss, a certain Colonel D.B. had phoned this Major already and we would have to go to the Major's office to collect the Army permit for Nathu-La

. We would be going there as "guests" of this Colonel D.B. Luckily, the Army camp was 5 minutes drive from our hotel and we quickly went there, and into the office of Major V. The Major took down our details, vehicle details and in a few minutes, got the permit ready. We were out of there soon after with an important piece of paper in our hands.
One still needs a govt issued vehicle permit from the permit office on top of this army permit, but since the army permit clearly mentions the vehicle details, the govt. vehicle permit is issued without question. It took us 15 minutes the next morning to get the vehicle permit and we were on our way.
After driving in Ladakh and Sandakphu, this drive was actually a piece of cake, but it was funny to see a single WB white plate vehicle moving single-file among all the yellow plated ones on the road to Nathu-La.
A big thanks to the INDIAN ARMY to make this possible for me.