SQL Server 2012 :: Incorporate RANK Or NTILE With LEAD Function?

We have accounts that pay for a particular "premium" service. It's entirely possible an account paid for this service for three consecutive months in 2013, then stopped paying, then started paying again. Why I'm trying to establish is, for the FIRST period of time the accout paid for this service, for how many consecutive months did they pay? Here is my test data:

if object_id('tempdb..#SampleData') is not null
drop table #SampleData
go
if object_id('tempdb..#DateAnalysis') is not null
drop table #DateAnalysis
go

-- Create temp tables for sample data

create table #SampleData
(AccountID int,
RandomDate datetime)
create table #DateAnalysis
(RowID int identity(1,1),
AccountID int,
RandomDate datetime,
NextDate datetime,
LeadInMonths int)

-- Insert some sample data

insert into #SampleData values
(1, '1/1/13'), (1, '2/1/13'), (1, '3/1/13'), (1, '6/1/13'), (1, '10/1/13'), (1, '11/1/13'), (1, '12/1/13'),
(2, '1/1/13'), (2, '4/1/13'), (2, '5/1/13'), (2, '6/1/13'),
(3, '2/1/13'), (3, '3/1/13'), (3, '4/1/13'), (3, '9/1/13'), (3, '10/1/13'), (3, '11/1/13')

-- Use lead function to determine how many months are between

-- consecutive dates per account

; with DateInterval as
(select AccountID, RandomDate,
NextDate = lead (RandomDate, 1, NULL) over (partition by AccountID order by RandomDate)
from #SampleData)
insert into #DateAnalysis
select AccountID, RandomDate, NextDate,
datediff(mm, RandomDate, NextDate) as 'Lead'
from DateInterval

where NextDate is not null -- Last row will contain NULL for NextDate. Don't include these rows.

-- Show the results

select *,
'NTile' = NTILE(3) over (partition by AccountID order by RandomDate),
'RowNum' = row_number() over (partition by AccountID order by RandomDate)
from #DateAnalysis

Results (this is not getting me what I'm looking for):

RowIDAccountIDRandomDateNextDateLeadInMonthsNTileRowNum
11 2013-01-012013-02-01111
21 2013-02-012013-03-01112
31 2013-03-012013-06-01323
41 2013-06-012013-10-01424
51 2013-10-012013-11-01135
61 2013-11-012013-12-01136
72 2013-01-012013-04-01311
82 2013-04-012013-05-01122

[code]....

This is what I'm trying to achieve:

RowIDAccountIDRandomDateNextDateLeadInMonthsRankForThisLeadInMonths
11 2013-01-012013-02-0111
21 2013-02-012013-03-0111
31 2013-03-012013-06-0132
41 2013-06-012013-10-0143
51 2013-10-012013-11-0114
61 2013-11-012013-12-0114

[code]....

The problem comes with accounts like AccountID = 1. They paid consecutively to start, then skipped, then started paying consecutively again. When using window functions, I'm running into trouble attempting to partition by AccountID and LeadInMonths. It's putting all the LeadInMonths = 1 together and that will give me skewed results if I want to know the earliest and latest date within the FIRST consecutive range of dates where the account paid. I've tried NTILE but it expects an integer and there's no telling how many "tiles" would be in AccountID partition.

I've looked at the OVER clause and the new "ROWS BETWEEN" syntax and still cannot get the desired results.