What are any and all of the exceptions to eating after noon if you've taken 8 precepts? Is broth and vegetable juice allowable? 

I am preferably looking for an answer by an experienced monk.
In order to understand the precept for lay people, it is useful to look at the rules for monks. For monks, there are four types of edible requisites, according to their lifetime:

1. Yavakalika

Solid food; including milk, soya milk, rice milk, etc.

This type can only be taken during the morning hours and may not be stored beyond noon of the day it was received.

2. yamakalika

Most types of uncooked, pulp-free fruit, vegetable, flower, root, or leaf juice.

This type can be taken any time of day, but only kept until dawn of the day after it was received.

3. satthahakalika

Medicinal tonics: ghee, oil, butter/cheese, honey and sugar.

This type can be taken any time of day by a monk who is sick in a way that will be assuaged by taking the tonic (usually stomach upset or hunger due to inability to keep food down). These may be kept for seven days.

4. yavajivaka

Anything normally considered as a medicine, within reason (any fruits, roots, flowers, bark, salts, etc. that are considered medicine by the world) 

This type can be taken any time of day provided there is a compelling reason (i.e. a sickness that is ameliorated by taking the medicine). They may be kept one's entire life.

The sixth precept probably follows the same pattern as the monastic practice (leaving aside the part about how long items may be kept), so unless one is sick, the only thing that can really be taken outside of the morning hours is uncooked, pulp-free fruit or vegetable juice. 

Tea, coffee, ginger, etc. are medicine and should only be taken if they are known to ameliorate a sickness one currently has.

Note that the five tonics can be useful for people unable to otherwise keep eight precepts due to health concerns. I once had an elderly student who was afraid to keep the eight precepts, and I suggested she try and if unable to take some butter. She was against the idea of taking butter due to its high cholesterol content, but I convinced her to try anyway. In the night, she sent a request for food so I had someone send her back a small butter pot. In the morning she came back all smiles, astonished at how well the butter worked to protect her stomach and feeling no adverse effects of keeping the precepts.