CCS/MSP430F5529: Timer_A1 not working properly with exernal clock source (P1.6)

I wrapped your code and ran it on an F5529 Launchpad, but I don't see the behavior you describe. I put a square wave at TA0 frequency out on P1.2, and patched it to P1.6, and TA1 counts correctly. If I connect P1.6 to GND, it doesn't count. 

I'm not sure what we're doing differently.

For reference (I compared TA0CNT0 with TA1R):

#include "driverlib.h"
int main(void)
{
    WDT_A_hold(WDT_A_BASE);
    GPIO_setAsPeripheralModuleFunctionInputPin(GPIO_PORT_P1, GPIO_PIN6); // TA1CLK

    Timer_A_initUpModeParam gTimerA0params = { 0 };
    Timer_A_initContinuousModeParam gTimerA1params = { 0 };

    // Timer_A0
    gTimerA0params.clockSource = TIMER_A_CLOCKSOURCE_ACLK; // Use ACLK as timer internal clock
    gTimerA0params.clockSourceDivider = TIMER_A_CLOCKSOURCE_DIVIDER_1; // Divide clock frequency by 1
    gTimerA0params.timerInterruptEnable_TAIE = TIMER_A_TAIE_INTERRUPT_DISABLE; // Timer interrupt disabled in TAxCTL Reg
    gTimerA0params.captureCompareInterruptEnable_CCR0_CCIE =
            TIMER_A_CAPTURECOMPARE_INTERRUPT_ENABLE; // Capture-Compare interrupt enabled in TAxCCTL0 Reg
    gTimerA0params.timerClear = TIMER_A_DO_CLEAR; // Clear time counter TAxR Reg
    gTimerA0params.startTimer = false;                // Do not start timer yet.
    gTimerA0params.timerPeriod = 500;                        // Set timer period
    // Clear pending interrupt (Clear flag TAIFG in TAxCTL Reg)
    Timer_A_clearTimerInterrupt(TIMER_A0_BASE);
    // Initialize TimerA0 with previous parameters
    Timer_A_initUpMode(TIMER_A0_BASE, &gTimerA0params);

    // *** Init TimerA1 ***
    gTimerA1params.clockSource = TIMER_A_CLOCKSOURCE_EXTERNAL_TXCLK; // Use P1.6 as external clock source
    gTimerA1params.clockSourceDivider = TIMER_A_CLOCKSOURCE_DIVIDER_1; // Divide clock frequency by 1
    gTimerA1params.timerInterruptEnable_TAIE = TIMER_A_TAIE_INTERRUPT_DISABLE; // Timer interrupt disabled in TAxCTL Reg
    gTimerA1params.timerClear = TIMER_A_DO_CLEAR; // Clear time counter TAxR Reg
    gTimerA1params.startTimer = false;                // Do not start timer yet.
    // Initialize TimerA1
    Timer_A_initContinuousMode(TIMER_A1_BASE, &gTimerA1params);

    //  Make something for TA1 to count
    //  Jumper P1.2 to P1.6 to see it count
    TA0CCR1 = TA0CCR0/2;      // 50% duty for no real reason
    TA0CCTL1 = OUTMOD_7;      // Reset/Set gives square wave
    P1SEL |= BIT2;            // Output TA0.1 on P1.2 per SLAS590N Table 6-46
    P1DIR |= BIT2;

    Timer_A_startCounter(TIMER_A0_BASE, TIMER_A_UP_MODE);
    Timer_A_startCounter(TIMER_A1_BASE, TIMER_A_CONTINUOUS_MODE);
    __enable_interrupt();
    LPM0;                     // Sleep forever
    return (0);
}
unsigned TA0CNT0;
#pragma vector=TIMER0_A0_VECTOR
__interrupt void TA0_CCR0_ISR(void)
{
    ++TA0CNT0;
    return;
}