But while there has hardly been a rush for the Cemeteries and Crematoria Services traineeship, the likes of Wednesday Addams and Eddie Munster need not apply.
"Working with bereavement is probably not that desirable for young people," concedes the council's Robin Leese. "But for the right calibre of person - someone who is caring and helpful - it can be very rewarding.
"There is far more to it than you would think. The job gives a great deal of satisfaction and it will always be required."
Wakefield launched the AMA last year, since when the first trainee - a 16-year-old girl - has proven a major success.
Mr Leese, 58, the council's cemeteries and crematoria manager and registrar, said: "We decided to set up the apprenticeship because we were concerned about the growing age profile of staff within the service. Other councils are watching the programme with interest."
He added: "There was not a great deal of interest last year. But the young girl we have had has fitted in very well indeed.
"It's a sensitive position and we look for the right calibre of person, someone who is probably a bit more sensible than their age and who can carry themselves with dignity."
With the first trainee now about to enter her second year, the council is looking for another young person. Initially, trainees are taught the administration involved in dealing with bereavement.
"We tend to shield them at first from the operational side of the business," Mr Leese said.
"But obviously the administration side can involve discussions about coffins and funeral arrangements. We only introduce them to the operational side as and when we think they are ready, extending their training to members of the public wanting memorials or helping with genealogical searches in cemeteries.
"In the second year of training, if the trainee is suitable, we involve them with the funeral process."
The successful applicant, who must have four GCSEs grade C minimum - including maths, English and a science subject - undertakes a national vocational qualification level 3 in administration one day a week at a local college to study for the recognised technical certificate in administration.
At the end of the two-year AMA, they can obtain the nationally-recognised professional qualification from the Institute of Burials and Cremation Authority.