I believe engineering is worse than accounting, but I have no first hand knowledge, so I will pass on that field. My understanding is that if the engineer hasn't progressed to management by the time they are twenty-five they have to go to sales.
As far as accounting goes, I can almost guarantee you, if you graduate with an accounting degree, you will not be hired. This was clearly made apparent to me by and Arthur Young principal at age 31 when I graduated, you are too old.
In the states the schools are turning out something like 60,000 degreed accountants a year. Everyone who is hiring is ( in their minds ) cherry picking. I understand Canada is worse and they are shipping their excess down here. Australia claims they have a shortage but they keep the age restrictions in place for immigrations, so I suspect they are also blowing smoke.
I've applied for jobs that were one step above starter and had to compete with 800 other qualified accountants.
When there is a shortage, employers don't play twenty questions and have two dozen secret attributes. This is the common situation with the present glut. Even the public accountants who get the fewest resumes ( if you ever worked for a public accountant you would understand why so few apply ) play these games.
I could go on but it is a waste of time, you have to find out these things for yourself.
Best of Luck.