Hello Mr Smith,
Good to hear that you have got your LEDs working OK.
That mod idea sounds like it could have a nice little effect. A simple circuit can be built which should achieve what you want with two ICs and a few external components. The circuit should blink up to 10 LEDs in sequence repeatedly. It can be expanded for a larger sequence, but it does become a little more complex. If you wanted more complex effects you could learn how to program a microcontroller

Here is a schematic:

I haven't tested it, only simulated. It should work though. Operation of the circuit is quite simple. I will attempt to explain the best I can.
C4 is a power supply filter capacitor. It should be rated at the very least 16v, capacitance isn't all that important. 10uF to 100uF should be fine, you can probably even get away without it if cost is an issue (although it should only be a couple of pennies).
C2 and C3 are decoupling / bypass capacitors. Unlike C4, these should be placed as close as you can to their respective ICs. Their purpose is to filter smaller fluctuations in the power supply. 10nF or 100nF should work I think. You may actually be able to get away without these for such a simple circuit.
The 555 timer, IC2, generates a square wave output ( something like ____|-----|____|-----|____ ) on pin 3. Pulling pin 4 high, to +12v in this case, takes the IC out of reset. C1 starts charging via R2 then through D1. R2 slows down the charging of this capacitor by limiting the current and this creates a 'time constant'.
Pin 2 (trigger) monitors the charging of C1. When the voltage is smaller than 1/3 of the supply it puts the output, pin 3, in to a high state of +12v.
Pin 6 also monitors this voltage, and when it reaches above 2/3rds of the supply it will put the output pin in to a low state of 0v and then connects the discharge pin, pin 7 to 0v. By connecting the discharge pin to 0v, the capacitor C1 starts to discharge through R1. It doesn't skip R2 like when charging, because the diode only conducts in one direction, so the discharging also happens slowly because discharge current is limited.
You may be able to see that this creates an endless loop of C1 charging and discharging, and thus flipping the output pin from 12v to 0v and vice versa at fixed periods. C1, R1 and R2 control timing.
The output pin of IC2 is connected to the clock pin of IC1. IC1 is a simple counter IC and is taken out of reset by pulling pin 15 low, to 0v. The clock input is enabled by pulling pin 13 high, to +12v. The outputs Q0 to Q9 should all start off in the low state. When a pulse is received on the clock pin, on the falling edge it will take the current output low and then toggle the next output high. So, starting off at Q0, it will take Q0 low and then Q1 high. On the next pulse it will take Q1 low, then Q2 high. When it reaches Q9 it simply starts the sequence over again, and so creates a chasing effect.
The small transistor circuit on Q0 should be repeated for each output pin (Q1 - Q9). This is here because the datasheet says the output pins can only handle up to 8mA of current each. A transistor needs only a small amount of current provided to the base to pass a large amount of current through the collector / emitter. The resistor R5 pulls the transistor low 'by default', and R4 limits the current to the base when the output pin goes high. The transistor acts like a electronic switch. When it has no base current, it is off and no current can pass. When it has some base current the transistor is switched on and current can flow from the LED to ground, thus lighting it up. R3 is the LED current limiting resistor.
Pins of ICs are easy to determine. Pin 1 will be indicated by a small circle / dimple on the casing. Opposite this will usually be the highest pin (eg for an 8 pin 555 opposite pin 1 will be pin 8). Then just count down / up for pin 2 - 7. For example:
1 8
2 7
3 6
4 5
As for the transistor pin out, if you hold it so that the flat side is facing toward you and pins going down toward the floor, then the pin on the left will be the emitter, the middle pin the base, and the pin on the right the collector. The emitter in the schematic symbol is represented by the small arrow pointing towards ground, and the collector is the pin with the LED connected to it. You should be able to work out which is the base

Pin outs can sometimes vary between different manufacturers, so it may be wise to search for data sheets just to make sure!
The time the 555 pulses last can be calculated by the following
Thi (s) = ( 0.7 x (R2 x C1) ) / 1,000,000
Tlo (s) = ( 0.7 x (R1 x C1) ) / 1,000,000
So for the values in the schematic (10k / 10k)
T = 0.7 x (10,000 x 47) / 1,000,000 = ~0.32 seconds.
You may want to include variable resistors to tweak the time. I don't recommend you simply replace R1 and R2 with variable resistors. You should leave R1 and R2 but reduce their value (~680R to 1k ish), then add a higher value (~100k) variable resistor in series with each resistor. So one VR between 12v and R2, and the other between pin 7 of the 555 and R1.
Hope that helps and wasn't too confusing!