How can I write a CTE in SQL Server to get the date from the preceding row for the person that has Type = NA.

If there are multiple preceding rows with NA then take the first one when sorted by dt_eff asc.

If there are any other types between start of record and type = NA then these records should be ignored. Only consider other Types for the same person when previous type is ended (Person 124 Scenario).

Source Data

Person    Type     dt_eff
123       A        2018-10-23 <Start of record >
123       NA       2018-11-19 <Should be the end date for above and don't select this in output> 
123       NA       2018-12-25 <don't select this in output>
124       A        2020-01-01 <Start of record >
124       B        2020-02-15 <Ignore and don't select in output>
124       NA       2020-05-14 <Should be the end date for start of record and don't select in op>
124       C        2020-10-13 <As the above start record has ended this should be new start>
124       NA       2021-01-15 <should be the end date for second start record>
124       A        2021-05-22 <As the above start record has ended this should be new start>
124       T        2021-08-22 <Ignored and don't select in output>
456       NA       2022-04-19 <Ignore as there is no leg record with valid type>
456       A        2022-05-01 <Start of record and null as end date as there is no type = NA>
456       B        2022-07-15 <Ignore>

Expected Output

Person    Type     dt_start     dt_end
123       A        2018-10-23   2018-11-19
124       A        2020-01-01   2020-05-14
124       C        2020-10-13   2021-01-15
124       A        2021-05-22   NULL
456       A        2022-05-01   NULL