Asked for male, 29 years old from Bangalore Rural
Generally speaking: 4th generation -- conclusive after 4 weeks (some say at 6).
3rd generation -- conclusive after 8 weeks (some would say 6+ weeks)
2nd generation -- conclusive after 10 - 12 weeks. The tests that could be deemed conclusive are 3rd generation tests and certainly 4th generation tests at 8 weeks. A 3rd generation test for the most part has to be done by a lab. All fda approved rapid tests are either 2nd generation tests or perform like 2nd generation tests in actual practice, even though they claim to be 3rd generation tests on paper. (recent exception might be the 4th generation test approved by the fda, but this is not widely used, yet.)
a positive test is conclusive at any period (though you'd check it by testing again with a different technology) but the negatives are more problematic. The later the test, the more reliable but a very few people remain negative for many months. At eight weeks a negative test has about a 97% reliability of truly being negative.