You need to buffer that output with a power stage. You can do that in many ways, using a relay is one of them, but I would not advise that.
A MOSFET power stage will be faster and more durable because there are no mechanical components.
As Alfred Centauri points out it is not starightforward to know why your npn design didnt work without an schematic, but Ill suggest a solution.
Ill assume is that you have an unregulated supply, and you are powering everything at 9V. This is enough to correctly bias any N channel MOSFET. What youll do is connect the output of your 555 directly to the mosfet's gate, the mosfet's source to gnd, and the mosfet's drain to the pump's negative terminal. And you will need two extra components, first and most important a 1n4007 diode in parallel with the pump, with the cathode on the pump's positive terminal. And also, a 1Meg resistor between the mosfet's gate and source.
The only thing you need to make sure is that the mosfet can handle the current needed by the pump. To do that, you need to measure the pump's current while connected to the battery directly. Now, you need a mosfet whose Rdson times that current squared (this will be the mosfet's on state power dissipation in your circuit) is less than the maximum power that the device can dissipate. For a TO220 Mosfet, that will be in the order of 0.5-1W depending on how hot you want it to run.
EDIT: The 1M pull-down is used to ensure that the MOSFET is properly switched off, draining the charge that may remain in the gate. Some might say that in this case it is not needed because the 555's output is push-pull, and can properly drive the gate to gnd. But I view this as decoupling caps, you always have to use them or you'll regret it. Besides, in this case there is a reason to use it; when power is removed, I wouldn't trust the 555 to drive the output low, and you want that MOSFET to turn off in that case. A G-S resistor is almost always a good idea.
How can I debug ... I see no voltage on pins 2,6 and 7 to ground.
If I understand correctly, those are all fed via R1 so I'd look closely for a dry joint at R1.
Even if C1 was shorted, I'd expect twiddling R2 would produce something measurable at pin 7.
If you disconnect power and pull the 555 out of the socket, I think you should probably be able to test c1,c2,r1,r2 in-circuit with a multimeter.
For example I'd expect resistance between socket positions 4 and 7 should be 1K
In general, when a circuit works with a device from one maker and not from another it is telling you is that your design is incorrectly using some feature of the device on the verge of the design characteristics.
In this case how you are driving the reset pin.
That is a bad thing. You say it works with a 555N, but I am willing to bet if you tested enough 555N samples, only a proportion of them will work. So be glad you tried the other part.
Fix your design so the reset pin gets what it really needs, i.e. a digital level not an analog voltage that hovers somewhere between the logic thresholds as defined in the worst case 555N/555P data-sheet.
You likely need to add a simple comparator circuit, with hysteresis, to do that.