Eddie has campaigned for Labour for many years - including canvassing and delivering leaflets. As other posters say, Eddie has stood to be on the party's National Executive Committee (NEC). Actually, I think that prior to Jeremy Corbyn's leadership, Eddie did serve one or two terms on the NEC. However, not being a Corbyn supporter (and having spoken out on anti-semitism), Eddie never won when Corbynistas and Momentum candidates were being elected to virtually every NEC position.
In my view, Eddie has earned the right to seek nomination as a Labour candidate. In most seats, there are many applicants to be the Labour candidate in national elections. My memory is that the rules state that the shortlist on which members vote for their preferred candidate must include at least one man and one woman. From memory, the shortlist is usually about 5 people.
The only potentially controversial situation would be if there was only one woman on the shortlist and that place was taken by Eddie. As with everyone, in deciding who to vote for, the party members would need to consider whether Eddie would ultimately be electable as an MP.
My view is that Eddie has certainly done enough to be considered as a candidate. However, it would not be in the spirit of all women shortlists for a high profile candidate to use rules devised to help women who in the past were often excluded from committees which decided who would be selected to stand as a Labour candidate.