Finding every occurance of a string

We are doing DNA research. We need to find all starting positions of a discreet string of characters within a larger string of characters. Below is a sample source string. Using FIND, we note that the first instance of TATAA from the left is at character 286. I think we can use the AGGREGATE formula (15 Small and 6 Ignore hidden values) to present all instances but I can't make it work. The ideal result would actually display the results from the right end of the source string. A result might be 6, 50, 75 (though that is not the case below). It doesn't matter if the list of occurences is presented in a column or row.

If you find a great answer, then you will be helping figure out one of the great mysteries of life.

Sample string (in cell B9)
GGGAGTGTTATTTTAATAAAATTGCTAGTTATTGTTGTAACGCATTCGTCTTATTCGAATCAAAACGACAATTTCTTCCTACTCAGTGTACATACATGAAAAAAATAACTGTTTAATACACGAAGGAAACACATTAACAATTCTGTTGCGAAAAATATAGCGTTGTAAATTTTGACATACGCTTATTTTTTAAAATAAGAAAGACGATTTCTCTATTTTTCTTGATATTTATCCTTCCGCAATTGTCGTGACAATTTGTTCTCTCCTCTTCTTCAAGGCAACGATTATAACACAGTTATTTGAATATCACTCAAGTGTAACGGTTTCGAGCTCTTCGATATTTTCACGTAGCACGCGCCTGTGATGTTCTAGTTCTTAGAAAAACATATAATAACGGAAAAACGTCTCACCTTTCGTTGTTCCGTTTTTCTGAATCTGTACTCGACACCCTGTACACCTTCATTACTTTCAATGCAATTCGGTTGTTCATACCAATATCACATTTCATATGGACTCTTATATGTCAACGATTTAGCGTAAAAGCATTATTCACTGCACTTCTGATGACGATGCGCGAATTAAATCTATAACAAACGTTGCATCAAAAACGTTGAGTTAAACAAAATATCGCGCAATTGAGACATAAACAAAAAAAAAACGAGATATTTTTGTCCATTTATTACGAAAGTAACTCGCGATGTTCTTCCGTCATTTGTAAGACAAGACATGTAATAATTTTTCTCTTACTGTTCGTGTGCGATATGAGCGCAACTGTGGAGTTAGATAGGTAGCGATGTACAAAACGTAACCATATAGTTTCTTGGTCAGAACAATTTGACACAATAGAGCACTTCTCCGCATTTTGCACTAATGCGTGCGTAAAGACGGGTTGACAAGCGGGTATACGTCCCGAGCTGAATAAAAAATAGATCCTGATACTTGCGTCGCGTCGACGTAGCGAGAGCGGGATCGGTTATTGACGACAGCTAGTAGTTAGTCA