...Also note that, as was revealed with JBrase was elected, the law is very flawed whenever unexpected things happen like a senator resigns.
Keep in mind that:
A - Homely does not BECOME a Senator until the end of the month. Can he resign from an office he does not hold?
B - Ignoring the above, the date he resigns can impact how long for the by-election by up to 6 days. Ideally he will speak to me in person and I can thumb though all the laws and explain to him exactly what would happen based on his decision.
A by-election can't take place until a vacancy occurs; and no vacancy can arise in homely's case until at least the start of the next Senate session. IMO, the new Senate can either expel homely early in the session; but the neatest solution would probably be a post-dated resignation by homely.
It's quite common for resignations to be stated as taking effect as of a specified time/date of the resigner's choosing. I can't see why that couldn't also be applicable for the current instance, e.g. homely specifying that he's resigning his office as of 12.01 on the date of swearing-in.