I agree that intermittent charging is better than continuous trickle charging. By "fast", I am assuming you mean a standard charge rate of ≤0.5C. NiMH do not do well with fast charge rates of several times C. The following applies to NiMH, unless stated otherwise.
I don't know of any evidence that shows a difference in long term performance between pulse charging to keep at full capacity, as described by Panasonic and Battery University, and regular charging when the battery reaches a certain state of discharge. The advantage of pulse charging is that the battery is always at full charge. However, if you set your recharge trigger to occur when, say 60% to 70% of charge remains, your alarm battery should still function well as the alarm and you will reduce the number of recharge cycles. eneloop batteries now carry a claim of 1500 cycles, which is large for NiMH. You can do the calculations from that. Self-discharge cannot be ignored with NiMH batteries, and I suggest you consider the newer, low-self-discharge batteries. I have experience with the Energizer mentioned above and eneloop. There is also a version from China with similar claims, but I have no experience with it.
As for your car battery, don't underestimate the effect of a slow drain on it. Here is a chart from Battery University (**broken link removed**
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A 50 mA discharge does not sound like much for a large car battery, but that is 1.2 Ah per day. If the car sits for 10 days, that is 12 Ah in addition to the normal self-discharge. That might not hurt an 80-Ah battery, but a smaller 20 Ah to 40 Ah starter battery will likely be damaged.
John