Search one string and then search another string in the next line

I am unable to use grep comman to Print only EmpPosition and if the EmpID next line. So output should be both EmpPosition and EmpID and also EmpPosition and EmpID data should match.

Sample Data

   EmpPosition "New"
       EmpID "New"
       
       -
       -
    EmpPosition "New"
     EmpName "XXXX"
     -
     -
    EmpPosition "old"
       EmpID "old"
           
           -
           -
    EmpPosition "old"
     EmpName "XXXX"
    -
    -
    EmpPosition "temp"
       EmpID "old"
           
           -
           -
    EmpPosition "old"
     EmpName "XXXX"
     
  Output    
     EmpPosition "New"
       EmpID "New"   
     EmpPosition "old"
       EmpID "old"
awk '/EmpPosition|EmpID/' infile

Some thing like this:

awk '/EmpPosition/ { c=1;a=$2;getline } c==1 && /EmpID/ { print a,$2;next} {c=0}' file

Neither of the suggestions above ensure the equality of EmpPosition and EmpID. Further, Jotne's solution does not ensure that the lines are consecutive.

Is whitespace allowed in the values to be tested for equality?

Regards,
Alister

---------- Post updated at 10:05 AM ---------- Previous update was at 09:54 AM ----------

Untested, but should work even if whitespace occurs in the quoted strings:

sed '/^[^"]*EmpPosition/!d; N; /\n[^"]*EmpID/!d; /^[^"]*\("[^"]*"\)[^"]*\1[^"]*$/!d' file

Regards,
Alister

awk version:

awk '$1=="EmpPosition"{p=$0; v=$2; getline; if($1=="EmpID" && v==$2) print p ORS $0}' file