To clearly understand the why and the how of "the third-person form of the verb with the - S dropped, in most cases", this file will be of a little help. Here it is. Take a look.

1. THE
SUBJUNCTIVE
By Kamol Karmakar
Lecturer, DELL,
USTC.

2. The Subjunctive in English is the simple/ base
form of the verb, used after certain expressions
that contain an order or a request, a hypothetical,
or a wish.

3. Subjunctive Verbs:
Urge Insist Advise Request
Ask Prefer Demand Move
Command Order Propose Require
Suggest Recommend Desire Stipulate

4. Sub (1) + subjunctive verb (any tense) + that +
sub (2) + base form of verb + extension
We advised that he study mindfully for the year
ending exams.
His parents have suggested that he buy this bag.
* In subjunctive sentences, the word ‘that’ appears,
if not the verbs are followed by the infinitive.
His parents have suggested him to buy this bag.

5. Subjunctive Adjectives:
Necessary Obligatory Suggested Advised
Important Mandatory Proposed Urgent
Recommended Imperative Required

6. It + be verbs (any tense) + subjunctive
adjective + that + sub + base form of verb +
extension
It is important that he attend the meeting.
It is urgent that he buy a shirt.

7. ‘Should’ as Subjunctive:
‘Should’ is most common after the verbs ‘suggest,’
‘recommend’ or ‘insist.’
* His teacher suggested that he should study harder
for the year ending exams.
* The doctor recommended that she should see a
gastroenterologist for her digestive problems.

8. Negative, Continuous and Passive Forms of
Subjunctive:
Negative Examples:
* The Principal asked that the teachers not
accept personal phone calls during class hours.
* They advised that I not take the job without
renegotiating the salary.

9. Negative, Continuous and Passive Forms of
Subjunctive:
Passive Examples:
* The Board requested that she be
prepared immediately for the national team
selection.
* The Head teacher ordered that the boy be
allowed to take part in the class.

10. Negative, Continuous and Passive Forms of
Subjunctive:
Continuous Examples:
* It is necessary that he be studying hard for the year
ending exams.
* I suggest that Leena be playing the guitar.

11. THANK YOU