First, the charging system is only rated at 3 Amps at 3,600 rpm. 3 Amps into a not-very-charged car battery isn't going to do a lot in terms of immediate terminal voltage, so I don't think your original test proved that there was a fault. I suggest you perform the Briggs-specified output current test:
System 3, 4 and Dual Circuit Alternators
Alternator Output Test Procedures
Test DC Amp Output
1. Insert RED test lead (3) into 10 A receptacle in
meter.
2. Insert BLACK test lead (2) into COM receptacle in
meter.
3. Rotate selector to (DC amps) position.
4. Attach RED test clip to stator output lead (4),
Fig. 16 (Typical).
See Fig. 17 for Dual Circuit alternator. The RED
wire (5) is DC output. The bump on the connector
indicates the DC output terminal (6)
5. Attach BLACK test clip (2) to the positive (+)
battery terminal or charging harness lead (1).
6. With engine running at specified RPM, output
should be as listed in Table No. 2, Specifications.
7. If low or no output, check stator air gap, when
applicable. See Table No. 2, Specifications.
8. If stator air gap is within specification and there is
low or no output, replace stator.
![[Linked Image]](https://www.outdoorking-forum.com.au/forum/uploads/usergals/2013/03/full-2772-10220-cox_stockman_11.5_hp_alternator_test.png)
Extract from Table No. 2 for your system (System 3 & 4):
DC Only Alternator and Dual Circuit Alternator
Output: Between 2 to 4 amps DC @3600 RPM.
Output will vary with battery voltage. At maximum
battery voltage, output should be approximately 2
amps.
If you do not get the specified current, we can talk about what to do next, which will be clean various terminals and set the alternator air gap.